Question

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

• A. 12
• B. $\frac{1}{12}$
• C. 11
• D. $\frac{1}{14}$

Answer 1

The correct option is B

$\frac{1}{12}$

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