Question

Express the following in exponential form :
${\left(\frac{-7}{8}\right)}^3$

Answer 1

$(\frac{-7}{8}{)}^3\Rightarrow (\frac{-7-1+1}{8}{)}^3\Rightarrow (\frac{-8+1}{8}{)}^3\Rightarrow (-1+\frac{1}{8}{)}^3$

$\Rightarrow (-1{)}^3+(\frac{1}{8}{)}^3+3(-1)\left(\frac{1}{8}\right)(-1+\frac{1}{8})$

$\Rightarrow -1+\frac{1}{8^3}+\frac{3}{8}\left[\frac{7}{8}\right]$

$\Rightarrow -1+8^{-3}+3^1\times 7^1\times 8^{-2}$

$(\frac{-7}{8}{)}^3=-1+2^{-3\times 3}+3^1\times 7^1\times 2^{-2\times 3}$

$(\frac{-7}{8}{)}^3=-1+2^{-9}+3\times 7\times 2^{-6}$