# How do you simplify (2x^2y)(5x^-2y^3) and write it using only positive exponents?

Jan 25, 2017

See the entire simplification process below:

#### Explanation:

First, rewrite the expression to group like terms:

$\left(2 \times 5\right) \left({x}^{2} \times {x}^{-} 2\right) \left(y \times {y}^{3}\right)$

Next further simplify using these two rules for exponents:

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

$\left(2 \times 5\right) \left({x}^{2} \times {x}^{-} 2\right) \left({y}^{\textcolor{red}{1}} \times {y}^{3}\right)$

$10 {x}^{2 + - 2} {y}^{1 + 3}$

$10 {x}^{0} {y}^{4}$

Now, use this rule for exponents to further simplify:

${a}^{\textcolor{red}{0}} = 1$

$10 \times 1 \times {y}^{4}$

$10 {y}^{4}$

There is no further simplification required as all of the exponents are positive.