Q. 140. - Intermediate Algebra

Question

In the following exercises, simplify each expression.

${\left(3y^2\right)}^4$

Step-by-Step Solution

Answer

The simplified form of the given expression is$81y^8$

Step 1. Given information. 3 y 2 4

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

Step 2. Calculation and simplification.

Calculation of expression using Product Property, 

$$\begin{gathered} {\left(3y^2\right)}^4 ={\left(3\right)}^4·{\left(y^2\right)}^4 \\ = 81·{\left(y^2\right)}^4 \end{gathered}$$

Now, We use power property

$$\begin{gathered} 81·{\left(y^2\right)}^4 = 81·y^{2·4} \\ = 81y^8 \end{gathered}$$

Therefore, the simplified form of the given expression is $81y^8$