# How do you simplify (m^7)^4*m^3 and write it using only positive exponents?

Mar 2, 2017

See the entire simplification process below:

#### Explanation:

First, use this rule for exponents to simplify the term on the left:

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

${\left({m}^{\textcolor{red}{7}}\right)}^{\textcolor{b l u e}{4}} {m}^{3} = {m}^{\textcolor{red}{7} \times \textcolor{b l u e}{4}} {m}^{3} = {m}^{28} {m}^{3}$

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

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

${m}^{\textcolor{red}{28}} {m}^{\textcolor{b l u e}{3}} = {m}^{\textcolor{red}{28} + \textcolor{b l u e}{3}} = {m}^{31}$