Question

In the following exercises, simplify each expression.

${\left(2m{n}^4\right)}^5$

Short answer

The simplified form of the given expression is $32m^5{n}^{20}$.

Step-by-step solution

Step 1. Given information.

The given expression ${\left(2m{n}^4\right)}^5$.

Step 2. Simplify the given expression.

Calculation of expression using Product Property

$$\begin{gathered} {\left(2m{n}^4\right)}^5={\left(2\right)}^5·{\left(m\right)}^5·{\left(n^4\right)}^5 \\ =32.m^5·{\left(n^4\right)}^5 \end{gathered}$$

Now, We use power property

$$\begin{gathered} 32.m^5·{\left(n^4\right)}^5=32m^5·n^{4.5} \\ =32m^5{n}^{20} \end{gathered}$$

Therefore, the simplified form of the given expression is$32m^5{n}^{20}$