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Answer: A

A negative exponent in a fraction leads to the reciprocal of the fraction. Thus the negative exponent of 2 is -2, allowing (2/3)^(-2) = (3/2)^2.
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(2/3)^n = (3/2)^2
= (2/3)^-2

n = -2 (Answer = A)
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jsphcal
If (2/3)^n=(3/2)^2, what is the value of n?

A. -2
B. -1
C. 0
D. 1
E. 2

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

Observe that 3/2 = (2/3)^-1. Then:

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

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

n = -2

Alternate Solution:

Let’s distribute the exponents to the numerator and the denominator:

2^n/3^n = 3^2/2^2

If we cross multiply, we have:

2^(n + 2) = 3^(n + 2)

We see that the exponents of 2 and 3 are equal. This is only possible if n + 2 = 0. Then, n = -2.

Answer: A
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Hello from the GMAT Club BumpBot!

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