Question

Simplify the following using laws of expressions
$(2x{)}^4÷(2x{)}^2$

Answer 1

Given that,

$\begin{array}{c}{\left(2x\right)}^4÷{\left(2x\right)}^2\\ =\frac{{\left(2x\right)}^4}{{\left(2x\right)}^2}\end{array}$

We know that,

$\begin{array}{c}\frac{x^a}{x^b}=x^{a-b}\\ \frac{{\left(2x\right)}^4}{{\left(2x\right)}^2}={\left(2x\right)}^{4-2}={\left(2x\right)}^2\\ ={\left(2x\right)}^2\end{array}$

We know that,

$\begin{array}{c}{\left(a.b\right)}^n=a^n{b}^n\\ =2^2{x}^2\\ 2^4=4\\ =4x^2\end{array}$

Then ,

We get $4x^2.$