Question

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

• A. 2
• B. $\frac{1}{12}$
• C. $\frac{2}{3}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B $\frac{1}{12}$

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