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Evaluate ( $\frac{1}{343}$ ) $^{\frac{1}{3}}$ + (64)\(^{-\f...

Evaluate ( $\frac{1}{343}$ ) $^{\frac{1}{3}}$ + (64) $^{-\frac{1}{3}}$ - $\frac{4}{9}$ $^{-\frac{1}{2}}$

A.

- $\frac{17}{36}$

B.

- $\frac{3}{28}$

C.

$\frac{31}{28}$

D.

$\frac{17}{36}$

E.

$\frac{1}{4}$

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Correct answer is C

( $\frac{1}{343}$ ) $^{\frac{1}{3}}$ + (64) $^{-\frac{1}{3}}$ - $\frac{4}{9}$ $^{-\frac{1}{2}}$

where $343 = 7^3, 64 = 2^6, 4 = 2^2, 9 = 3^2$

$7^{-3}$ $^{\frac{1}{3}}$ + $2^6$ $^{\frac{-1}{3}}$ - $\frac{2^2}{3^2}$ $^{\frac{-1}{2}}$

$7^{-1} + 2^{-2} - (\frac{2}{3})^{-1}$

$\frac{1}{7} + \frac{1}{4} - \frac{3}{2}$

$\frac{4+7-42}{28}$

$\frac{31}{28}$

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