Question

Simplify, giving solution with positive index​ : (xvii) $\left(2a^3{)}^4\right(4a^2{)}^2$

Answer 1

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

On further calculation , we have

$\left(2a^3{)}^4\right(4a^2{)}^2=2^4{a}^{3\times 4}.2^{2\times 2}.a^{2\times 2}$

[$\because$ $(a^m{)}^n=a^{mn}$]

$=2^4{a}^{12}.2^4{a}^4$ [$\because$ $a^m\times a^n=a^{m+n}$]
$=2^{4+4}{a}^{12+4}$
$=2^8{a}^{16}$
$=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times a^{12}=256a^{12}$

Hence, $\left(2a^3{)}^4\right(4a^2{)}^2=256a^{12}$