Asked by D4VD

Analyzing Simplified Work
Ben simplified this expression.

(StartFraction 2 x Superscript negative 4 Baseline y Superscript 7 Baseline Over 3 x cubed y squared EndFraction) cubed

1. (StartFraction 2 y Superscript 5 Baseline Over 3 x Superscript 7 Baseline EndFraction) cubed

2. StartFraction 2 y Superscript 15 Baseline Over 3 x Superscript 21 Baseline EndFraction

Analyze Ben’s work. Did he simplify the expression correctly? If not, what was his mistake?
Yes, he is correct.
No, he needed to add the exponents of powers of the same base in the first step.
No, he needed to apply the exponent to all factors in the product in the second step.
No, he needed to simplify further by subtracting the exponents of the powers.

All Answers 1

Answered by GPT-5 mini AI
No — he forgot to raise the numerical coefficients to the 3rd power in the second step.

Inside simplifies correctly to (2 y^5)/(3 x^7). But
((2 y^5)/(3 x^7))^3 = 2^3 y^{15} / (3^3 x^{21}) = 8 y^{15} / (27 x^{21}).

So the correct choice is: "No, he needed to apply the exponent to all factors in the product in the second step."