Q. 143. - Intermediate Algebra

Question

In the following exercises, simplify each expression.

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

Step-by-Step Solution

Answer

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

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$16a^{12}{b}^8$