Consider the exponential expression (y^7)^3. If this expression is rewritten in the equiva… — Armed Services Vocational Aptitude Battery (ASVAB)

Consider the exponential expression $(y^7)^3$ . If this expression is rewritten in the equivalent form $y^n$ , what is the numerical value of $n$ ?

Answer: 21 / twenty-one / n=21 / n = 21

Answer

The numerical value of the exponent is 21.

When raising a power to another power, the laws of exponents dictate that the two exponents must be multiplied. Multiplying the inside exponent 7 by the outside exponent 3 yields 21.

Step-by-Step Solution

Identify the appropriate exponent rule to simplify the expression

(y^7)^3

The expression requires the Power of a Power property.

An exponential term with a base and an exponent is being raised entirely to another power.

Apply the Power of a Power rule, which states that

(x^a)^b = x^{a \times b}

Multiply the inner exponent by the outer exponent:

7 \times 3

To raise a power to another power, you must multiply the exponents together.

Calculate the final numerical value.

7 \times 3 = 21

, meaning the expression simplifies to

y^{21}

By matching

y^{21}

to the given form

y^n

, we determine that

n = 21

Key Concept

Power of a Power Rule for Exponents

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