Algebra Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 10

Soru 181Soru →

A network engineer is configuring a load balancer to distribute traffic across two servers. The equation below models the traffic distribution, where $t$ represents the number of active connections:

5(2t - 4) - 3t = 4(t + 2) - (t - 8)

Calculate the required number of active connections, $t$ , to successfully balance the server loads.

Cevabı ve açıklamayı göster

Cevap: 9

Cevap

9

By successfully applying the distributive property on both sides, combining the variable and constant terms, and isolating the variable, the equation perfectly balances when the variable is exactly 9.

Adım Adım Çözüm

1

Distribute the coefficients and negative signs across the parentheses on both sides of the equation.

10t - 20 - 3t = 4t + 8 - t + 8

Distribution removes the parentheses, allowing individual terms to be combined.

2

Combine like terms on each side of the equation.

7t - 20 = 3t + 16

Simplifying each side individually makes it easier to balance the equation.

3

Subtract

3t

from both sides of the equation.

4t - 20 = 16

This groups all the variable terms on one side of the equation.

4

Add 20 to both sides and divide by 4.

4t = 36 \implies t = 9

Isolating the variable determines the final numerical solution.

Anahtar Kavram

Solving multi-step linear equations involving the distributive property and combining like terms.

Soru 182Soru →

What is the product of the binomials $(2x - 1)$ and $(x + 4)$ ?

2x^2 - 4

2x^2 - 7x - 4

2x^2 + 7x - 4

9x^3 - 4

Cevabı ve açıklamayı göster

Cevap: $2x^2 + 7x - 4$

Cevap

The correct expression is

2x^2 + 7x - 4

.

By applying the FOIL method, we multiply the First terms to get

2x^2

, the Outer terms to get

8x

, the Inner terms to get

-x

, and the Last terms to get

-4

. Combining the like terms

8x

and

-x

results in the simplified polynomial

2x^2 + 7x - 4

.

Adım Adım Çözüm

1

Multiply the First terms.

2x \times x = 2x^2

This is the 'F' step in the FOIL method.

2

Multiply the Outer terms.

2x \times 4 = 8x

This is the 'O' step in the FOIL method.

3

Multiply the Inner terms.

-1 \times x = -x

This is the 'I' step in the FOIL method.

4

Multiply the Last terms.

-1 \times 4 = -4

This is the 'L' step in the FOIL method.

5

Combine the resulting terms.

2x^2 + 8x - x - 4 = 2x^2 + 7x - 4

Combine the like middle terms (

8x

and

-x

) to simplify the final expression.

Anahtar Kavram

Multiplying binomials using the distributive property (FOIL method) and combining like terms.

Soru 183Soru →

Match each unsimplified algebraic expression on the left with its equivalent fully simplified form on the right. Assume all variables represent non-zero real numbers.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The product rule matches to -12a^6/b^3, the quotient rule matches to 2b^4/a^4, the power of a product rule matches to 16a^12b^20, and the negative exponent simplification matches to a^4/25.

Matching each pair correctly requires correctly identifying and applying four distinct fundamental laws of exponents: the product rule (adding exponents), the quotient rule (subtracting exponents), the power of a product rule (multiplying exponents), and the rules for evaluating zero and negative exponents.

Adım Adım Çözüm

1

Simplify

(3a^4b^2)(-4a^2b^{-5})

using the product rule for exponents.

-12a^6b^{-3}

, which simplifies to

\frac{-12a^6}{b^3}

.

When multiplying expressions with the same base, add their exponents and multiply their numerical coefficients.

2

Simplify

\frac{16a^3b^6}{8a^7b^2}

using the quotient rule for exponents.

2a^{-4}b^4

, which simplifies to

\frac{2b^4}{a^4}

.

When dividing expressions with the same base, subtract the denominator's exponent from the numerator's exponent and divide the numerical coefficients.

3

Simplify

(2a^3b^5)^4

using the power of a product rule.

16a^{12}b^{20}

.

When raising a product to a power, raise the numerical coefficient to that power and multiply each variable's exponent by the outer power.

4

Simplify

(5a^{-2}b^0)^{-2}

using the zero and negative exponent rules.

First,

b^0 = 1

. Then evaluate

5^{-2}a^4

, which simplifies to

\frac{a^4}{25}

.

Any non-zero term raised to the zero power equals 1. Negative exponents indicate the reciprocal of the base.

Anahtar Kavram

Operations with Variable Exponents

Soru 184Soru →

If $4(k - 3) = 28$ , what is the value of $k$ ?

Cevabı ve açıklamayı göster

Cevap: 10

Cevap

10

Applying inverse operations to isolate the variable results in

k = 10

. This can be verified by substituting 10 back into the original equation:

4(10 - 3) = 4(7) = 28

, which makes the statement true.

Adım Adım Çözüm

1

Divide both sides by 4.

k - 3 = 7

Dividing by the coefficient outside the parentheses simplifies the equation and isolates the binomial.

2

Add 3 to both sides of the equation.

k = 10

Using the inverse operation of subtraction isolates the variable

k

.

Anahtar Kavram

Solving One-Variable Linear Equations

Soru 185Soru →

An aircraft's current cruising altitude is $a$ feet. The required altitude for a new training maneuver is defined as four hundred feet less than triple the sum of the current altitude and two thousand. Which of the following algebraic expressions represents the required altitude in feet?

3(a + 2000) - 400

400 - 3(a + 2000)

3a + 2000 - 400

3(2000a) - 400

Cevabı ve açıklamayı göster

Cevap: $3(a + 2000) - 400$

Cevap

The correct expression is

3(a + 2000) - 400

.

The correct answer accurately models the sequence of operations described in the text. It uses parentheses to group the addition

(a + 2000)

, multiplies that entire group by 3, and places the subtraction of 400 at the end of the expression to correctly satisfy the 'less than' condition.

Adım Adım Çözüm

1

Translate 'the sum of the current altitude and two thousand'.

(a + 2000)

The word 'sum' indicates addition between the variable

a

and the number 2000. Parentheses are required because subsequent operations apply to this entire result.

2

Apply the multiplier 'triple' to the sum.

3(a + 2000)

'Triple' means multiplying the entire grouped quantity by 3.

3

Incorporate the phrase 'four hundred feet less than'.

3(a + 2000) - 400

The phrase 'less than' is a turnaround phrase, meaning the 400 must be subtracted from the previously established quantity.

Anahtar Kavram

Translating multi-step verbal phrases into algebraic expressions requires careful attention to grouping symbols and translation order, particularly for subtraction.

Soru 186Soru →

Calculate the product of the two algebraic terms below:

-4m^3 \times 3m^4

What is the correct result of this multiplication?

-12m^7

12m^7

-12m^{12}

12m^{12}

Cevabı ve açıklamayı göster

Cevap: $-12m^7$

Cevap

The correct answer is

-12m^7

.

To multiply these terms, first multiply the numerical coefficients:

-4 \times 3 = -12

. Then, apply the product rule for exponents by adding the exponents of the common base

m

:

3 + 4 = 7

. Combining these yields

-12m^7

.

Adım Adım Çözüm

1

Multiply the numerical coefficients.

-4 \times 3 = -12

When multiplying algebraic terms, the constant factors are multiplied together using standard integer rules.

2

Apply the product rule for exponents to the variables.

m^3 \times m^4 = m^{3+4} = m^7

The product rule states that when multiplying terms with the same base, their exponents should be added.

3

Combine the coefficient and the variable part.

-12m^7

Putting the results from the previous steps together gives the final simplified expression.

Anahtar Kavram

Product Rule for Exponents and Multiplying Monomials

Tahmini Süre:45s

Soru 187Soru →

Calculate the intermediate and final values for the given algebraic expression.

Aşağıdaki boşlukları doldurun

To evaluate the expression

5x - y^2

for

x = 3

and

y = -4

, we first substitute the given numbers. The term

5x

evaluates to . The term

y^2

evaluates to . Subtracting the second result from the first gives a final answer of .

Cevabı ve açıklamayı göster

Cevap

The intermediate values are 15 and 16, resulting in a final answer of -1.

Substituting the given values into the expression

5x - y^2

yields

5(3) - (-4)^2

. Following the order of operations, first evaluate the exponent:

(-4)^2 = 16

. Next, perform the multiplication:

5(3) = 15

. Finally, perform the subtraction:

15 - 16 = -1

.

Adım Adım Çözüm

1

Substitute x = 3 into the first term, 5x.

5(3) = 15

Variable substitution replaces the variable with its assigned numerical value.

2

Substitute y = -4 into the second term, y^2.

(-4)^2 = 16

Squaring a negative number results in a positive value, since negative multiplied by negative is positive.

3

Subtract the evaluated second term from the evaluated first term.

15 - 16 = -1

The original expression requires subtracting the y^2 term from the 5x term.

Anahtar Kavram

Evaluating Algebraic Expressions

Soru 188Soru →

Determine the value of $y$ that makes the following equation true:

6y - 12 = 36

Which of the following represents the correct value of $y$ ?

42

4

8

-6

Cevabı ve açıklamayı göster

Cevap: 8

Cevap

The correct value of y is 8.

The correct value is 8. To isolate the variable y, the constant 12 must first be added to both sides of the equation, which results in 6y = 48. Finally, dividing both sides by the coefficient 6 gives the solution y = 8.

Adım Adım Çözüm

1

Add 12 to both sides of the equation.

6y = 36 + 12 \Rightarrow 6y = 48

This isolates the term with the variable on one side of the equation.

2

Divide both sides by 6.

y = \frac{48}{6} \Rightarrow y = 8

This isolates the variable y and provides the final solution.

Anahtar Kavram

Solving two-step linear equations by performing inverse operations.

Soru 189Soru →

During a physics calculation, a student models a system's energy output using the following expression, where $x$ and $y$ are non-zero variables:

\frac{(2x^{-2}y^3)^3}{4x^{-4}y^5}

What is the fully simplified form of this expression using only positive exponents?

\frac{2y^4}{x^2}

\frac{2y^4}{x^{10}}

\frac{y^4}{2x^2}

\frac{3y^4}{2x^2}

Cevabı ve açıklamayı göster

Cevap: $\frac{2y^4}{x^2}$

Cevap

\frac{2y^4}{x^2}

Applying the power of a product rule to the numerator yields

8x^{-6}y^9

. Dividing this by the denominator

4x^{-4}y^5

involves dividing the coefficients (

8/4 = 2

) and subtracting the exponents of like bases. For

x

,

-6 - (-4) = -2

, and for

y

,

9 - 5 = 4

. The resulting expression is

2x^{-2}y^4

. To represent this with positive exponents, the

x^{-2}

term is moved to the denominator, giving

\frac{2y^4}{x^2}

.

Adım Adım Çözüm

1

Apply the power of a product rule to the numerator.

(2x^{-2}y^3)^3 = 2^3 \cdot (x^{-2})^3 \cdot (y^3)^3 = 8x^{-6}y^9

The exponent outside the parentheses applies to every individual factor inside.

2

Divide the numerical coefficients.

8 \div 4 = 2

Numerical coefficients are handled separately from variables with exponents.

3

Apply the quotient of powers rule to the variables.

x^{-6 - (-4)} = x^{-2}

and

y^{9 - 5} = y^4

When dividing like bases, you subtract the denominator's exponent from the numerator's exponent.

4

Combine the results and convert the negative exponent to a positive exponent.

2x^{-2}y^4 = \frac{2y^4}{x^2}

Moving a term with a negative exponent to the denominator changes its exponent to positive.

Anahtar Kavram

Simplifying rational algebraic expressions using the power of a product rule, the quotient of powers rule, and negative exponents.

Soru 190Soru →

Match each verbal phrase or word problem to its correct algebraic equation translation.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The correct matches pair each verbal description with its mathematically equivalent equation by carefully translating order of operations, rates, geometric formulas, and grouping words.

Each verbal phrase uniquely defines a single algebraic relationship. By identifying key terms such as 'less than' for reverse-order subtraction, rate contexts for variable multiplication, geometric formulas for perimeter, and grouping words for parentheses, each scenario is mapped accurately to its corresponding equation.

Adım Adım Çözüm

1

Analyze the first phrase: 'Eight less than five times a number

x

is equal to twenty.'

Translates to

5x - 8 = 20

.

'Five times a number' is

5x

. The phrase 'less than' dictates that 8 is subtracted from

5x

.

2

Analyze the second phrase: 'A service charges 8 dollars per hour plus a 5 dollar flat fee. The total cost for

x

hours is 20 dollars.'

Translates to

8x + 5 = 20

.

The variable

x

is multiplied by the hourly rate of 8, and the one-time flat fee of 5 is added to this product.

3

Analyze the third phrase: 'The perimeter of a rectangle is 20. Its length is 5 units more than its width,

x

.'

Translates to

2x + 2(x + 5) = 20

.

The perimeter formula is

2W + 2L

. Substituting

x

for width and

(x + 5)

for length provides the correct equation.

4

Analyze the fourth phrase: 'Five times the difference of a number

x

and eight results in twenty.'

Translates to

5(x - 8) = 20

.

The word 'difference' combined with 'times' indicates that the subtraction

(x - 8)

must occur first, requiring parentheses before multiplying by 5.

Anahtar Kavram

Translating complex word phrases into algebraic equations requires strict attention to operation order, grouping symbols, and contextual formulas.

Soru 191Soru →

Determine the value of the unknown variable in the following linear equation.

Aşağıdaki boşlukları doldurun

Solve the equation for

m

:

4m - 7 = 13

The correct value for

m

is .

Cevabı ve açıklamayı göster

Cevap

The value of the variable m is 5.

Applying the inverse operation by adding 7 to both sides gives

4m = 20

. Dividing by 4 isolates the variable, resulting in the correct value of 5.

Adım Adım Çözüm

1

Add 7 to both sides of the equation.

4m = 13 + 7 \Rightarrow 4m = 20

To isolate the term with the variable (

4m

) on one side of the equation.

2

Divide both sides by 4.

m = \frac{20}{4} \Rightarrow m = 5

To solve for

m

by canceling out its coefficient.

Anahtar Kavram

Solving one-variable linear equations by applying inverse operations to isolate the variable.

Soru 192Soru →

Calculate the value of the algebraic expression $x^2 - 4y$ given that $x = -5$ and $y = -2$ . What is the final value?

Cevabı ve açıklamayı göster

Cevap: 33

Cevap

33

By correctly applying substitution and the order of operations, squaring

-5

gives

25

, and multiplying

4

by

-2

gives

-8

. Subtracting

-8

from

25

results in

33

.

Adım Adım Çözüm

1

Substitute the given variable values into the expression

(-5)^2 - 4(-2)

To replace the variables with their corresponding numerical values.

2

Evaluate the exponent

25 - 4(-2)

Following the order of operations (PEMDAS), exponents must be calculated before multiplication and subtraction. The square of a negative number is positive.

3

Evaluate the multiplication

25 - (-8)

Multiply 4 by -2 to find the term to be subtracted.

4

Perform the final subtraction

25 + 8 = 33

Subtracting a negative number is equivalent to adding its positive counterpart.

Anahtar Kavram

Evaluating Algebraic Expressions

Soru 193Soru →

Multiply the binomials $(x - 5)$ and $(x + 2)$ . Fill in the missing values for the resulting expanded expression $x^2 + bx + c$ .

Aşağıdaki boşlukları doldurun

The value of

b

is .
The value of

c

is .

Cevabı ve açıklamayı göster

Cevap

The value of b is -3 and the value of c is -10.

By applying the FOIL method, you multiply the First terms (

x \times x = x^2

), Outer terms (

x \times 2 = 2x

), Inner terms (

-5 \times x = -5x

), and Last terms (

-5 \times 2 = -10

). Combining the like terms (

2x - 5x

) results in

-3x

. The fully expanded expression is

x^2 - 3x - 10

. Comparing this to the standard form

x^2 + bx + c

, we find that the coefficient for the middle term

b

is

-3

and the constant term

c

is

-10

.

Adım Adım Çözüm

1

Use the FOIL method to distribute the terms in the binomials.

(x \times x) + (x \times 2) + (-5 \times x) + (-5 \times 2)

Each term in the first binomial, including its sign, must be multiplied by each term in the second binomial.

2

Perform the multiplications for each pair.

x^2 + 2x - 5x - 10

This expands the product using the rules for multiplying positive and negative numbers.

3

Combine the like terms.

x^2 - 3x - 10

Adding the middle terms (

2x

and

-5x

) simplifies the expression into the standard form

x^2 + bx + c

.

Anahtar Kavram

Multiplying Polynomials

Soru 194Soru →

Calculate the value of

x

that satisfies the given equation:

7x - 14 = 21

Which of the following represents the correct value?

1

-3

5

-5

Cevabı ve açıklamayı göster

Cevap: 5

Cevap

5

The correct answer is 5. To solve the equation, the first step is to add 14 to both sides, which balances the equation and gives 7x = 35. The final step is dividing both sides by 7 to isolate the variable, resulting in x = 5.

Adım Adım Çözüm

1

Add 14 to both sides of the equation.

7x = 21 + 14

7x = 35

This isolates the term with the variable by removing the constant on the left side.

2

Divide both sides by 7.

x = 5

This solves for x by reversing the multiplication by 7.

Anahtar Kavram

Solving One-Variable Linear Equations requires isolating the variable using inverse operations.

Soru 195Soru →

Simplify the following algebraic expression, assuming all variables are non-zero:

\frac{(3m^2n^4)^2}{3m^5n^3}

Which of the following represents the fully simplified form?

\frac{3n^5}{m}

\frac{n^5}{m}

3m^9n^{11}

\frac{3m}{n^5}

Cevabı ve açıklamayı göster

Cevap: $\frac{3n^5}{m}$

Cevap

The fully simplified expression is

\frac{3n^5}{m}

.

The correct expression is derived by properly applying the power rules. First, squaring the numerator

(3m^2n^4)^2

yields

9m^4n^8

. Then, dividing this by the denominator

3m^5n^3

requires dividing the coefficients (

9/3 = 3

) and subtracting the exponents of corresponding variables (

4-5 = -1

for

m

, and

8-3 = 5

for

n

). Finally, rewriting

3m^{-1}n^5

with only positive exponents gives

\frac{3n^5}{m}

.

Adım Adım Çözüm

1

Simplify the numerator using the power of a product rule.

(3m^2n^4)^2 = 3^2 \cdot (m^2)^2 \cdot (n^4)^2 = 9m^4n^8

When a product is raised to a power, each factor inside the parentheses must be raised to that power.

2

Substitute the simplified numerator back into the fraction.

\frac{9m^4n^8}{3m^5n^3}

This sets up the expression for applying the quotient rules.

3

Divide the numerical coefficients.

\frac{9}{3} = 3

Constants are simplified through standard division.

4

Apply the quotient rule for exponents to the variables

m

and

n

.

m^{4-5} = m^{-1}

and

n^{8-3} = n^5

When dividing terms with the same base, subtract the exponent in the denominator from the exponent in the numerator.

5

Combine the results and rewrite without negative exponents.

3m^{-1}n^5 = \frac{3n^5}{m}

A negative exponent indicates the reciprocal of the base, moving the term to the denominator.

Anahtar Kavram

Exponent rules including power of a power, power of a product, and quotient of powers.

Soru 196Soru →

What is the expanded form of the product $(a - 3)(a + 7)$ ?

a^2 - 21

a^2 + 4a - 21

a^2 - 4a - 21

a^2 - 17a

Cevabı ve açıklamayı göster

Cevap: $a^2 + 4a - 21$

Cevap

a^2 + 4a - 21

The expression is properly expanded by distributing each term in the first binomial to each term in the second binomial, resulting in

a^2 + 7a - 3a - 21

. Combining the like terms (

7a - 3a

) yields the final simplified polynomial

a^2 + 4a - 21

.

Adım Adım Çözüm

1

Multiply the first terms in each binomial.

a \times a = a^2

To begin distributing the first term of the first binomial.

2

Multiply the outer terms.

a \times 7 = 7a

To complete the distribution of the first term.

3

Multiply the inner terms.

-3 \times a = -3a

To begin distributing the second term of the first binomial.

4

Multiply the last terms in each binomial.

-3 \times 7 = -21

To complete the distribution of the second term.

5

Combine the like middle terms to simplify the expression.

7a + (-3a) = 4a

To write the polynomial in its fully simplified standard form, resulting in

a^2 + 4a - 21

.

Anahtar Kavram

Multiplying Binomials

Soru 197Soru →

Solve for $n$ in the equation below:

8n - 11 = 37

Enter the exact value of $n$ .

Cevabı ve açıklamayı göster

Cevap: 6

Cevap

6

To find the value of

n

, first perform the inverse operation of subtraction by adding 11 to both sides, which simplifies the equation to

8n = 48

. Then, perform the inverse operation of multiplication by dividing both sides by 8, yielding

n = 6

.

Adım Adım Çözüm

1

Isolate the variable term.

8n = 48

Adding 11 to both sides neutralizes the -11 on the left side of the equation.

2

Solve for the variable.

n = 6

Dividing both sides by 8 isolates n completely.

Anahtar Kavram

Solving two-step linear equations using inverse operations.

Soru 198Soru →

Translate the following verbal statement into algebraic expressions representing each side of the equation:

'Eleven less than three times a number, $q$ , is equal to five times the sum of the number and two.'

Aşağıdaki boşlukları doldurun

The expression for 'Eleven less than three times a number,

q

' is:

The expression for 'five times the sum of the number and two' is:

Cevabı ve açıklamayı göster

Cevap

The left expression is 3q - 11 and the right expression is 5(q + 2).

The verbal phrase 'less than' requires the subtracted amount to follow the term it modifies, making the first expression 3q - 11. The phrase 'times the sum of' explicitly requires multiplying by a grouped addition, making the second expression 5(q + 2).

Adım Adım Çözüm

1

Translate the phrase representing the left side of the equation: 'Eleven less than three times a number,

q

'.

3q - 11

The phrase 'three times a number,

q

' translates directly to 3q. The phrase 'less than' dictates that 11 is subtracted from 3q, reversing the apparent reading order of the words.

2

Translate the phrase representing the right side of the equation: 'five times the sum of the number and two'.

5(q + 2)

The phrase 'sum of the number and two' translates to (q + 2). Grouping symbols (parentheses) are required because the multiplication by five applies to the entire sum, not just the first term.

Anahtar Kavram

Translating complex algebraic phrases by correctly applying order-reversing terminology and grouping indicators.

Tahmini Süre:1m 0s

Soru 199Soru →

If the equation

\frac{(3x^4 y^k)^2}{x^3 y^5} = 9x^5 y^{11}

is true for all non-zero values of

x

and

y

, what is the value of

k

?

Cevabı ve açıklamayı göster

Cevap: 8; k=8; k = 8

Cevap

8

By applying the power rule to expand the numerator, the expression becomes

9x^8 y^{2k}

. Using the quotient rule to divide these terms by the denominator

x^3 y^5

, the expression simplifies to

9x^5 y^{2k-5}

. Equating this final simplified form to the given result

9x^5 y^{11}

, we can isolate the exponent of

y

to set up the equation

2k - 5 = 11

. Solving this equation gives

k = 8

.

Adım Adım Çözüm

1

Apply the power of a product and power of a power rules to the numerator.

(3x^4 y^k)^2 = 3^2 (x^4)^2 (y^k)^2 = 9x^8 y^{2k}

When a product is raised to a power, each factor inside the parentheses must be individually raised to that power by multiplying the exponents.

2

Substitute the expanded numerator back into the fraction and apply the quotient rule.

\frac{9x^8 y^{2k}}{x^3 y^5} = 9 x^{8-3} y^{2k-5} = 9x^5 y^{2k-5}

When dividing algebraic terms with the same base, subtract the exponent of the denominator from the exponent of the numerator.

3

Equate the simplified exponent of

y

to the exponent of

y

on the right side of the original equation.

2k - 5 = 11

Because the expressions are equivalent and their coefficients and

x

-terms already match, their

y

-exponents must be strictly equal.

4

Solve the resulting linear equation for

k

.

2k = 16 \rightarrow k = 8

Adding 5 to both sides and then dividing by 2 isolates the variable

k

.

Anahtar Kavram

Operations with Variable Exponents

Tahmini Süre:1m 30s

Soru 200Soru →

Follow the steps to evaluate the algebraic expression given the variable assignments. What are the intermediate and final values?

Aşağıdaki boşlukları doldurun

For the expression

p^3 - 6q

, given that

p = -2

and

q = 3

:

The value of the first term,

p^3

, is .
The value of the second term,

6q

, is .
The final evaluated result of the entire expression is .

Cevabı ve açıklamayı göster

Cevap

The intermediate values are -8 and 18, which subtract to a final result of -26.

By accurately substituting

p = -2

and

q = 3

into the given expression, applying the exponent correctly, and performing the final subtraction, we arrive at the correct values for each step and the final answer of -26.

Adım Adım Çözüm

1

Substitute the given value for

p

into the first term.

(-2)^3 = -8

Replacing the variable

p

with

-2

evaluates the exponent. A negative base raised to an odd power remains negative.

2

Substitute the given value for

q

into the second term.

6(3) = 18

Replacing the variable

q

with

3

completes the multiplication required for the second term.

3

Combine the evaluated terms according to the original expression.

-8 - 18 = -26

Following the original expression

p^3 - 6q

, we subtract the value of the second term from the first term.

Anahtar Kavram

Evaluating algebraic expressions involving exponents and negative numbers

Tahmini Süre:45s

Algebra

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