Question

Simplify, giving solution with positive index​ : (xv) $-\left(3ab{)}^2\right(-5a^{2}b{c}^4{)}^2$

Answer 1

Given , $-\left(3ab{)}^2\right(-5a^{2}b{c}^4{)}^2$
It can be written as:

$-\left(3^2{a}^2{b}^2\right)\times (-1{)}^2\times 5^2{a}^{2\times 2}{b}^2{c}^{4\times 2}$ [$\because$ $(a^m{)}^n=a^{mn}$]

On further calculation , we have

$\left(3^2{a}^2{b}^2\right)\left(5^2{a}^4{b}^2{c}^8\right)=-3^2{.5}^2.a^{2+4}{b}^{2+2}{c}^8$
[$\because$ $a^m\times a^n=a^{m+n}$]

$=-225a^6{b}^4{c}^8$

Hence, $-\left(3ab{)}^2\right(-5a^{2}b{c}^4{)}^2=-225a^6{b}^4{c}^8$