Question

In the following exercises, simplify each expression.

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

Short answer

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

Step-by-step solution

Step 1. Given information. 3y24

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 $81y^8$