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If (2/3)^n=(9/4)^2, what is the value of n?

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by Max@Math Revolution » Wed Aug 15, 2018 6:36 am

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[Math Revolution GMAT math practice question]

If (2/3)^n=(9/4)^2, what is the value of n?

A. -4
B. -2
C. 0
D. 2
E. 4
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by Max@Math Revolution » Fri Aug 17, 2018 1:17 am
=>

(9/4)^2 = ((3/2)^2)^2 = (3/2)^4 = (2/3)^{-4}.
Thus, n = -4.

Therefore, the answer is A.

Answer: A
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by Jeff@TargetTestPrep » Mon Aug 20, 2018 10:46 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If (2/3)^n=(9/4)^2, what is the value of n?

A. -4
B. -2
C. 0
D. 2
E. 4

Using the negative exponent rule, we have:

[(3/2)^-1]^n = [(3/2)^2]^2

(3/2)^-n = (3/2)^4

-n = 4

n = -4

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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