Question

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

• A. $\frac{12}{13}$
• B. $\frac{13}{12}$
• C. $\frac{11}{16}$
• D. $\frac{16}{11}$

Answer 1

The correct option is C

$\frac{11}{16}$

$\because a^{-n}=\frac{1}{a^n}fora\ne 0$
$⟹(\frac{1}{5}{)}^{-3}=\frac{1}{(\frac{1}{5}{)}^3}=(\frac{5}{1}{)}^3=5^3=125$
Similarly, $(\frac{1}{3}{)}^{-4}=\frac{1}{(\frac{1}{3}{)}^4}=(\frac{3}{1}{)}^4=3^4=81$ and
$(\frac{1}{4}{)}^{-3}=\frac{1}{(\frac{1}{4}{)}^3}=(\frac{4}{1}{)}^3=4^3=64$

$⟹\frac{(\frac{1}{5}{)}^{-3}-(\frac{1}{3}{)}^{-4}}{(\frac{1}{4}{)}^{-3}}=\frac{125-81}{64}=\frac{44}{64}=\frac{11}{16}$