Question

Simplify:
$\frac{(-2{)}^3\times (-2{)}^7}{3\times 4^6}$

Answer 1

$\frac{(-2{)}^3\times (-2{)}^7}{3\times 4^6}=\frac{(-2{)}^{3+7}}{3\times (2^2{)}^6}$
Because $\{a^m\times a^n=a^{m+n}\}$,
$=\frac{(-2{)}^{10}}{3\times 2^{12}}\left\{\right(a^m{)}^n=a^{m\times n}\}$
$=\frac{(-2{)}^{10}}{3\times 2^{12}}=\frac{2^{10-12}}{3}\{a^m÷a^n=a^{m-n}and(-2{)}^{10}=2^{10}\}$
$=\frac{2^{-2}}{3}=\frac{1}{3\times 2^2}=\frac{1}{12}$