Q. 145. - Intermediate Algebra

Question

In the following exercises, simplify each expression.

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

Step-by-Step Solution

Answer

The simplified form of the given expression is $\frac{8}{27}{x}^6{y}^3$

Step 1. Given information.

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

Step 2. Simplify the given expression.

Calculation of expression using product property,

$$\begin{gathered} {\left(\frac{2}{3}{x}^{2}y\right)}^3 = {\left(\frac{2}{3}\right)}^3·{\left(x^2\right)}^3·y^3 \\ = \frac{8}{27}·{\left(x^2\right)}^3·y^3 \end{gathered}$$

Now we use the power property, 

$$\begin{gathered} \frac{8}{27}·{\left(x^2\right)}^3·y^3 = \frac{8}{27}·x^{2.3}·y^3 \\ = \frac{8}{27}{x}^6{y}^3 \end{gathered}$$

Therefore, the simplified form of the given expression is $\frac{8}{27}{x}^6{y}^3$