# How do you use the laws of exponents to simplify the expression b^8(2b)^7?

Jun 30, 2018

See a solution process below:

#### Explanation:

First, use this rule of exponents to rewrite the term within the parenthesis:

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

${b}^{8} {\left(2 b\right)}^{7} \implies {b}^{8} {\left({2}^{\textcolor{red}{1}} {b}^{\textcolor{red}{1}}\right)}^{7}$

Now, use this rule of exponents to eliminate the need for parenthesis:

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

${b}^{8} {\left({2}^{\textcolor{red}{1}} {b}^{\textcolor{red}{1}}\right)}^{\textcolor{b l u e}{7}} \implies {b}^{8} {2}^{\textcolor{red}{1} \times \textcolor{b l u e}{7}} {b}^{\textcolor{red}{1} \times \textcolor{b l u e}{7}} \implies {b}^{8} {2}^{7} {b}^{7} \implies {b}^{8} 128 {b}^{7}$

Now, rewrite the expression and use this rule of exponents to complete the simplification:
${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

${b}^{8} 128 {b}^{7} \implies 128 {b}^{\textcolor{red}{8}} \times {b}^{\textcolor{b l u e}{7}} \implies 128 {b}^{\textcolor{red}{8} + \textcolor{b l u e}{7}} \implies 128 {b}^{15}$