If ( 45)^n=( 54)^3, what is the value of n? | GMAT Sprint

Free Practice Question

PS · Problem Solving

sub-505

Exponents/Powers

If $(\frac{4}{5})^n=(\frac{5}{4})^3$ , what is the value of n?

Answer Choices

Correct answer marked below

-3

Correct

-2

-1

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Explanation

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Official Explanation

Official

Given that

(\frac{5}{4})^3=(\frac{4}{5})^{-3}

, we can rewrite the equation as…

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Comments

TanApr 27, 2024

thanks a lot

SRISHTIOct 21, 2024

good question

WeeJun 24

easy one, just flip the right side and you can see n right away

BhavyaJul 1

yeah flipping (5/4)^3 to (4/5)^-3 makes it obvious

SebastianMay 6

wait can someone explain why the answer isn't 3? i keep getting confused with the negative sign on the exponent

TanishaMay 14

think of it this way: (4/5) raised to a positive power stays small, but (5/4)^3 is bigger than 1. so n has to be negative to flip it

SameerApr 17

thanks, helpful

AyushJun 7

sub-505 but i still second-guessed myself lol. the reciprocal exponent rule always trips me up for a second

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 (45)n=(54)3(\frac{4}{5})^n=(\frac{5}{4})^3(54​)n=(45​)3, what is the value of n?