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If $(\frac{2}{3})^{m} (\frac{3}{4})^{n} = \frac{256}{729}$ ...

If $(\frac{2}{3})^{m} (\frac{3}{4})^{n} = \frac{256}{729}$ , find the values of m and n.

A.

m = 4, n = 2

B.

m = -4, n = -2

C.

m = -4, n =2

D.

m = 4, n = -2

E.

m = -2, n = 4

View answer & explanation

Correct answer is D

( $\frac{2}{3}$ )m ( $\frac{3}{4}$ )n = $\frac{256}{729}$

$\frac{2^m}{4^n}$ x $\frac{3^n}{3^m}$ = $\frac{2^{8}}{3^{6}}$

$2^{m} \div 2^{2n} = 2^{8}; 3^{n} \div 3^{m} = 3^{-6}$

m - 2n = 8........(i)

-m + n = -6........(ii)

Solving the equations simultaneously

m = 4, n = -2

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