Given the equation 2^(3x+2)*3^(3y-2) = 16^x*8… | GMAT Sprint

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Given the equation $2^{(3x+2)}3^{(3y-2)} = 16^x81^y$ , what is the value of x + y?

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Correct answer marked below

-4

-2

Correct

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Explanation

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Official Explanation

Official

To solve

2^{(3x+2)}*3^{(3y-2)} = 16^x*81^y

, we first rewrite the right-hand side. We know that

16 = 2^4

and

81 = 3^4

, so

16^x = 2^{4x}

and

81^y = 3^{4y}

. Therefore, the equation becomes…

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Comments

suryanshJan 26, 2024

Thank for sharing!!!

DevanshFeb 25, 2024

thanks!

MariahSep 6

thanks, this one was quick once I rewrote 16 and 81 as powers of 2 and 3

IshanSep 15

yeah same, that was the whole trick basically

HassanAug 3

wait how do you handle the exponents after rewriting? do you match the bases?

ShruthiApr 16

small trap: 81^y is 3^(4y) not 3^(3y), caught me for a sec

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).

Given the equation 2(3x+2)∗3(3y−2)=16x∗81y2^{(3x+2)}*3^{(3y-2)} = 16^x*81^y2(3x+2)∗3(3y−2)=16x∗81y, what is the value of x + y?