Question

Simplify, giving solution with positive index​ : $\left({10}^{10}{)}^{10}\right(1^6{)}^{10}$.

Answer 1

Given , $\left({10}^{10}{)}^{10}\right(1^6{)}^{10}$.
It can be written as:
$\left({10}^{10}{)}^{10}\right(1^6{)}^{10}={10}^{10\times 10}.1^{6\times 10}$ [$\because$ $(a^m{)}^n=a^{mn}$]

On further calculation , we have

$\left({10}^{10}{)}^{10}\right(1^6{)}^{10}={10}^{100}.1^{60}=a^{100}$

Hence, $\left({10}^{10}{)}^{10}\right(1^6{)}^{10}={10}^{100}$