# How do you simplify u^3v^2*(uv^2)^3 and write it using only positive exponents?

Feb 6, 2017

See the entire simplification process below:

#### Explanation:

First, use these two rules for exponents to expand the term terms within parenthesis:

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

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${u}^{3} {v}^{2} \cdot {\left(u {v}^{2}\right)}^{3} \to {u}^{3} {v}^{2} \cdot {\left({u}^{\textcolor{red}{1}} {v}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{3}} \to {u}^{3} {v}^{2} \cdot \left({u}^{\textcolor{red}{1} \cdot \textcolor{b l u e}{3}} {v}^{\textcolor{red}{2} \cdot \textcolor{b l u e}{3}}\right) \to$

${u}^{3} {v}^{2} \cdot {u}^{3} {v}^{6}$

Next, rewrite the expression to group like terms:

${u}^{3} {u}^{3} \cdot {v}^{2} {v}^{6}$

Now, use this rule of exponents to complete the simplification.

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

${u}^{\textcolor{red}{3}} \times {u}^{\textcolor{b l u e}{3}} \cdot {v}^{\textcolor{red}{2}} \times {v}^{\textcolor{b l u e}{6}} = {u}^{\textcolor{red}{3} + \textcolor{b l u e}{3}} {v}^{\textcolor{red}{2} + \textcolor{b l u e}{6}} =$

${u}^{6} {v}^{8}$

Because there are no negative exponents there is no further simplification needed.