Question

Simplify, giving solution with positive index​ (xix) $(\frac{1}{2x}{)}^3\times (6x{)}^2$.

Answer 1

Given , $(\frac{1}{2x}{)}^3\times (6x{)}^2$
It can be written as :

$(\frac{1}{2x}{)}^3\times (6x{)}^2=\frac{1^3}{2^3\times x^3}\times 6^2\times x^2$

[$\because$ $(\frac{a}{b}{)}^m=\frac{a^m}{b^m},(ab{)}^m=a^m{b}^m$]

$\frac{6\times 6}{2\times 2\times 2\times x}=\frac{36}{8x}=\frac{9}{2x}$ [$\because$ $a^{-m}=\frac{1}{a^m}$]

Hence, $(\frac{1}{2x}{)}^3\times (6x{)}^2=\frac{9}{2x}$ .