Question

Simplify, giving solution with positive index​ : (xii) $\left({10}^2{)}^3\right(x^8{)}^{12}$

Answer 1

Given , $\left({10}^2{)}^3\right(x^8{)}^{12}$
It can be written as:
$\left({10}^2{)}^3\right(x^8{)}^{12}={10}^{2\times 3}{x}^{8\times 12}$ [$\because$ $(a^m{)}^n=a^{mn}$]

On further calculation , we have

$\left({10}^2{)}^3\right(x^8{)}^{12}={10}^6{x}^{96}$

Hence, $\left({10}^2{)}^3\right(x^8{)}^{12}={10}^6{x}^{96}$.