How do you simplify (4a^3)^2 and write it using only positive exponents?

Apr 7, 2017

See the entire simplification process below:

Explanation:

Use these two rules of exponents to simplify this expression:

$a = {a}^{\textcolor{red}{1}}$ and ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left(4 {a}^{3}\right)}^{2} = {\left({4}^{\textcolor{red}{1}} {a}^{\textcolor{red}{3}}\right)}^{\textcolor{b l u e}{2}} = {4}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}} {a}^{\textcolor{red}{3} \times \textcolor{b l u e}{2}} = {4}^{2} {a}^{6} = 16 {a}^{6}$

Apr 7, 2017

color(blue)(16a^6

Explanation:

${\left(4 {a}^{3}\right)}^{2}$

$\therefore {\left({m}^{m}\right)}^{n} = {m}^{m \times n}$

$\therefore {4}^{2} {a}^{6}$

:.color(blue)(16a^6