Question

Using laws of exponents , simplify : ${\left(\frac{5y}{{\left(4x\right)}^2}\right)}^3$

Answer 1

Given that, : ${\left(\frac{5y}{{\left(4x\right)}^2}\right)}^3$

$=\frac{{\left(5y\right)}^3}{{\left({\left(4x\right)}^2\right)}^3}$

$=\frac{5^3\times y^3}{{\left(4x\right)}^{2\times 3}}$ [ Using laws of exponent : $a^n\times a^m=a^{m+n}$ , ${\left(a^n\right)}^m=a^{mn}$ and $a^{-n}=\frac{1}{a^n}$]

$=\frac{5^3\times y^3}{{\left(4x\right)}^6}$

$=5^3\times y^3\times {\left(4x\right)}^{-6}$

$=5^3\times y^3\times 4^{-6}\times x^{-6}$

$=\frac{125y^3}{4096x^6}$

Hence, required value is $\frac{125y^3}{4096x^6}$ .