Question

Using laws of exponents , simplify : $\frac{{\left(2x^2\right)}^3}{{\left(5x\right)}^{-2}}$

Answer 1

Given that, $\frac{{\left(2x^2\right)}^3}{{\left(5x\right)}^{-2}}$

$={\left(2x^2\right)}^3\times {\left(5x\right)}^2$

$=2^3\times {\left(x^2\right)}^3\times 5^2\times x^2$ [ Using laws of exponent : $a^n\times a^m=a^{m+n}$ , ${\left(a^n\right)}^m=a^{mn}$ and $a^{-n}=\frac{1}{a^n}$]

$=8\times x^6\times 25\times x^2$

$=200x^8$

Hence, required value is $200x^8$ .