# How do you simplify 7x^3y^2*5xy^9 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 together:

$\left(7 \times 5\right) \left({x}^{3} \times x\right) \left({y}^{2} \times {y}^{9}\right)$

Next, use these two rules for exponents to simplify the expression:

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

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

The expression then transforms as:

$\left(7 \times 5\right) \left({x}^{3} \times {x}^{\textcolor{red}{1}}\right) \left({y}^{2} \times {y}^{9}\right)$

$35 {x}^{3 + 1} {y}^{2 + 9}$

$35 {x}^{4} {y}^{11}$

Because the exponents are already positive there is no need for any more simplification.