Question

Simplify[(2x)^x(2x)^(2x)]^(1/x)

Answer 1

`\mleft[\mleft(2x\mright)^x\mleft(2x\mright)^(2x)\mright]^{(1)/(x)}`

We have the expression above

we will use two of the laws of exponents in order to simplify the expression

`x^m\cdot x^n=x^(m+n)`
`(x^m)^n=x^(m\cdot n)`

using these two laws we will have

`\begin{gathered} \lbrack(2x)^x(2x)^(2x)\rbrack^{(1)/(x)}=\lbrack(2x)^(x+2x)\rbrack^{(1)/(x)}=\lbrack(2x)^(3x)\rbrack^{(1)/(x)}=(2x)^{3x\cdot(1)/(x)}=(2x)^3=2^3x^3 \\ =8x^3 \end{gathered}`

the simplification is

`\lbrack(2x)^x(2x)^(2x)\rbrack^{(1)/(x)}=8x^3`