Question

Evaluates the following.
$\frac{{\left(\frac{12}{13}\right)}^5\times {\left(\frac{-1}{3}\right)}^6}{\frac{1}{81}\times {\left(\frac{12}{13}\right)}^3}$

Answer 1

Given:

$\frac{(\frac{12}{13}{)}^5\times (\frac{-1}{3}{)}^6}{\frac{1}{81}\times (\frac{12}{13}{)}^3}=\frac{(\frac{12}{13}{)}^2\times (\frac{1}{3}{)}^6}{(\frac{1}{3}{)}^4}$ (since, $\frac{a^m}{a^n}=a^{m-n}$)

$=(\frac{3\times 4}{13}{)}^2\times (\frac{1}{3}{)}^2$ (since, $\frac{a^m}{a^n}=a^{m-n}$)

$=(\frac{4}{13}{)}^2=0.0947$ (since, $\frac{a^m}{a^n}=a^{m-n}$)