Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Simplify the following expression.

${\left(\frac{2w^2{z}^5}{3y^4}\right)}^3$

F$\frac{2w^5{z}^8}{3y^7}$

G$\frac{8w^6{z}^{15}}{27y^{12}}$

H$\frac{8w^5{z}^8}{27y^7}$

J$\frac{2w^6{z}^{15}}{3y^{12}}$

Short answer

The value of the given expression${\left(\frac{2w^2{z}^5}{3y^4}\right)}^3$ is $\frac{8w^6{z}^{15}}{27y^{12}}$. Therefore, the option G is correct.

Step-by-step solution

Step 1. Write the property of power of a product, power of a quotient and power of a power. 

The property of power of a product states that:

${\left(ab\right)}^m=a^m{b}^m$

The property of power of a quotient states that:

${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

The property of power of a power states that:

${\left(a^m\right)}^n=a^{mn}$

Step 2. Simplify the given expression.

The value of the given expression${\left(\frac{2w^2{z}^5}{3y^4}\right)}^3$ after simplification is:

role="math" localid="1647682531721" $$\begin{gathered} {\left(\frac{2w^2{z}^5}{3y^4}\right)}^3=\frac{{\left(2w^2{z}^5\right)}^3}{{\left(3y^4\right)}^3}\left(\text{powerofaquotient}\right) \\ =\frac{2^3{\left(w^2\right)}^3{\left(z^5\right)}^3}{3^3{\left(y^4\right)}^3}\left(\text{powerofaproduct}\right) \\ =\frac{8w^{2\times 3}{z}^{5\times 3}}{27y^{4\times 3}}\left(\text{powerofapower}\right) \end{gathered}$$

Therefore, the value of the given expression${\left(\frac{2w^2{z}^5}{3y^4}\right)}^3$ is $\frac{8w^6{z}^{15}}{27y^{12}}$. Therefore, the option G is correct.