Question

In the following exercises, simplify each expression.

${\left(y^4\right)}^3.{\left(y^5\right)}^2$

Short answer

The simplified form of the given expression is$y^{22}$.

Step-by-step solution

Step 1. Given information. 

The given expression is ${\left(y^4\right)}^3·{\left(y^5\right)}^2$.

Step 2. Apply the power and product property.

Use the power property, $a^{m^n}=a^{m+n}$

And, use the Product Property, localid="1661185985403" $a^m·a^n=a^{m+n}$

Calculation of expression using power property,

localid="1661185971084" $y^{4·3}·y^{5·2}=y^{12}·y^{10}$

Now use the product property,

localid="1661185978445" $$\begin{gathered} y^{12}·y^{10}=y^{12+10} \\ =y^{22} \end{gathered}$$