Question

Simplify, giving solution with positive index​ : (xiv) $\left(n^2{)}^2\right(-n^2{)}^3$.

Answer 1

Given , $\left(n^2{)}^2\right(-n^2{)}^3$
It can be written as:

$\left(n^2{)}^2\right(-n^2{)}^3=n^{2\times 2}\times (-1)n^6$ [$\because$ $(a^m{)}^n=a^{mn}$]

On further calculation , we have

$\left(n^2{)}^2\right(-n^2{)}^3=n^4\times (-1)n^6=n^4\times (-1)n^6$

$=-n^{4+6}$ [$\because$ $a^m\times a^n=a^{m+n}$]

$=-n^{10}$

Hence, $\left(n^2{)}^2\right(-n^2{)}^3=-n^{10}$.