Question

Using laws of exponents , simplify : ${\left(6a^2{b}^2\right)}^3+{\left(3a^2\right)}^4$

Answer 1

Given that, ${\left(6a^2{b}^2\right)}^3+{\left(3a^2\right)}^4$

$=\left(6^3\times a^{2\times 3}\times b^{2\times 3}\right)+\left(3^4\times a^{2\times 4}\right)$

$=216a^6{b}^6+81a^8$

[ Using laws of exponent : $a^n\times a^m=a^{m+n}$ , ${\left(a^n\right)}^m=a^{mn}$ and $a^{-n}=\frac{1}{a^n}$]

$=27a^6\left(8b^6+3a^2\right)$

Hence, required value is $27a^6\left(8b^6+3a^2\right)$ .