# What is the expression (x^2z^3)(xy^2z) is equivalent to?

Aug 19, 2017

#### Answer:

See a solution process below:

#### Explanation:

We can rewrite the expression as:

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

Next, we can use these rules of exponents to multiply the $x$ and $z$ terms:

$a = {a}^{\textcolor{b l u e}{1}}$ and ${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\left({x}^{2} \cdot x\right) {y}^{2} \left({z}^{3} \cdot z\right) \implies$

$\left({x}^{\textcolor{red}{2}} \cdot {x}^{\textcolor{b l u e}{1}}\right) {y}^{2} \left({z}^{\textcolor{red}{3}} \cdot {z}^{\textcolor{b l u e}{1}}\right) \implies$

${x}^{\textcolor{red}{2} + \textcolor{b l u e}{1}} {y}^{2} {z}^{\textcolor{red}{3} + \textcolor{b l u e}{1}} \implies$

${x}^{3} {y}^{2} {z}^{4}$