Q. 142. - Intermediate Algebra

Question

In the following exercises, simplify each expression.

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

Step-by-Step Solution

Answer

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

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 $32m^5{n}^{20}$