If 4^(m + 2) = 16^(m − 3), then m = | GMAT Sprint

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PS · Problem Solving

sub-505

Exponents/Powers

If $4^{(m + 2)} = 16^{(m − 3)}$ , then $m =$

Answer Choices

Correct answer marked below

−8

-6

Correct

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Explanation

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Official Explanation

Official

Given:

4^{(m + 2)} = 16^{(m − 3)}

. Rewrite

16

4^2

to get:

4^{(m + 2)} = (4^2)^{(m − 3)}

. Apply the Power of a Power law: [m]4^{(m +…

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Comments

ChristianJan 6, 2024

Tricky wording but good practice

유

유진Oct 16, 2024

cheers!

YosefJul 5

thanks, this one was pretty quick once you see 16 is just 4 squared

AdityaJul 15

yep that's the whole trick, then just match the exponents

AliAug 10

wait why do we convert 16? cant we just plug the answers in?

SaranchanaAug 11

you could, but rewriting 16 as 4^2 is way faster. plugging all 5 choices would eat time on the real thing

What this question tests

What it tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Common trap

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).

If 4(m+2)=16(m−3)4^{(m + 2)} = 16^{(m − 3)}4(m+2)=16(m−3), then m=m =m=