Simplify (15)−3−(13)−4(14)−3.

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Question

Simplify $\frac{(\frac{1}{5})^{- 3} - (\frac{1}{3})^{- 4}}{(\frac{1}{4})^{- 3}} .$

Options:

A .

\frac{12}{13}

B .

\frac{13}{12}

C .

\frac{11}{16}

D .

\frac{16}{11}

Answer: Option C
:
C

$∵ a^{- n} = \frac{1}{a^{n}} f o r a \neq 0$
$⟹ (\frac{1}{5})^{- 3} = \frac{1}{(\frac{1}{5})^{3}} = (\frac{5}{1})^{3} = 5^{3} = 125$
Similarly, $(\frac{1}{3})^{- 4} = \frac{1}{(\frac{1}{3})^{4}} = (\frac{3}{1})^{4} = 3^{4} = 81$ and
$(\frac{1}{4})^{- 3} = \frac{1}{(\frac{1}{4})^{3}} = (\frac{4}{1})^{3} = 4^{3} = 64$
$⟹ \frac{(\frac{1}{5})^{- 3} - (\frac{1}{3})^{- 4}}{(\frac{1}{4})^{- 3}} = \frac{125 - 81}{64} = \frac{44}{64} = \frac{11}{16}$

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