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Question:
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$\left\{\left(\frac{1}{3}\right)^{-3}-\left(\frac{1}{2}\right)^{-3}\right\} \div\left(\frac{1}{4}\right)^{-3}=?$

(a) $\frac{19}{64}$

(b) $\frac{27}{16}$

(c) $\frac{64}{19}$

(d) $\frac{16}{25}$

Solution:

(a) $\frac{19}{64}$

$\left\{\left(\frac{1}{3}\right)^{-3}-\left(\frac{1}{2}\right)^{-3}\right\} \div\left(\frac{1}{4}\right)^{-3}$

$=\left\{3^{3}-2^{3}\right\} \div 4^{3}$

$=\{27-8\} \div 64$

$=19 \div 64$

$=\frac{19}{64}$

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