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Simplify; [( $\frac{16}{9}$ ) $^{\frac{-3}{2}}$ x 16\(^{\fr...

Simplify; [( $\frac{16}{9}$ ) $^{\frac{-3}{2}}$ x 16 $^{\frac{-3}{4}}$ ] $^{\frac{1}{3}}$

A.

$\frac{3}{4}$

B.

$\frac{9}{16}$

C.

$\frac{3}{8}$

D.

$\frac{1}{4}$

View answer & explanation

Correct answer is C

[( $\frac{16}{9}$ ) $^{\frac{-3}{2}}$ x 16 $^{\frac{-3}{4}}$ ] $^{\frac{1}{3}}$

= [( $\frac{9}{16}$ )] $^{\frac{3}{2}}$ x [( $\frac{1}{16}$ ) $^{\frac{3}{4}}$ ] $^{\frac{1}{3}}$

= [( $\sqrt{\frac{9}{10}}$ ) $^3$ x (4 $\sqrt{\frac{1}{16}})^3$ ] $^{\frac{1}{3}}$

= [( $\frac{3}{4})^3 \times (\frac{1}{2})^3$ ] $^\frac{1}{3}$

( $\frac{27}{64} \times \frac{1}{8}$ ) $^\frac{1}{3}$ = ${3}\sqrt{\frac{27}{64} \times \frac{1}{8}}$

= $\frac{3}{4} \times \frac{1}{2}$ = $\frac{3}{8}$

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