Question

In the following exercises, simplify each expression.

${\left(-2a^3{b}^2\right)}^4$

Short answer

The simplified form of the given expression is$16a^{12}{b}^8$

Step-by-step solution

Step 1. Given information. 

The given expression is ${\left(-2a^3{b}^2\right)}^4$.

Step 2. Simplify the given expression.

Calculation of expression using product property,

$$\begin{gathered} {\left(-2a^3{b}^2\right)}^4={\left(-2\right)}^4·{\left(a^3\right)}^4·{\left(b^2\right)}^4 \\ =16·{\left(a^3\right)}^4·{\left(b^2\right)}^4 \end{gathered}$$

Now we use the power property

$$\begin{gathered} 16·{\left(a^3\right)}^4·{\left(b^2\right)}^4=16·a^{3.4}·b^{2.4} \\ =16a^{12}{b}^8 \end{gathered}$$

Therefore, the simplified form of the given expression is$16a^{12}{b}^8$