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Question

Difficulty: EasyOperations with Variable Exponents

Simplify the following algebraic expression:

(3y4)(−5y2)(3y^4)(-5y^2)

Which of the following is the correctly simplified expression?

  1. A
    15y615y^6
  2. −15y6-15y^6Answer
  3. C
    −15y8-15y^8
  4. D
    −2y6-2y^6

Answer

−15y6-15y^6
The expression is simplified by first multiplying the numerical coefficients (3×−5=−153 \times -5 = -15). Then, the product rule for exponents is applied to the variables by adding their exponents (y4×y2=y4+2=y6y^4 \times y^2 = y^{4+2} = y^6). Combining these two parts yields the correct simplified expression, −15y6-15y^6.

Step-by-Step Solution

1
Group and multiply the numerical coefficients.
3×(−5)=−153 \times (-5) = -15
The commutative property allows us to group the constant numbers together for multiplication.
2
Multiply the variable terms using the product rule for exponents.
y4×y2=y4+2=y6y^4 \times y^2 = y^{4+2} = y^6
When multiplying exponential terms with the same base, their exponents must be added.
3
Combine the resulting coefficient and variable term.
−15y6-15y^6
This represents the final simplified form of the expression.

Key Concept

Product Rule for Exponents and Integer Multiplication
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Topics

Operations with Variable Exponents

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