How do you simplify [(4r^2t)^3]^2?

Feb 8, 2017

See the entire simplification process below:

Explanation:

First, simplify the outer brackets using this rule for exponents:

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

${\left[{\left(4 {r}^{2} t\right)}^{\textcolor{red}{3}}\right]}^{\textcolor{b l u e}{2}} = {\left(4 {r}^{2} t\right)}^{\textcolor{red}{3} \times \textcolor{b l u e}{2}} = {\left(4 {r}^{2} t\right)}^{6}$

Now we can use the above rule and this rule to complete the simplification:

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

${\left(4 {r}^{2} t\right)}^{6} = {\left({4}^{\textcolor{red}{1}} {r}^{2} {t}^{\textcolor{red}{1}}\right)}^{6} = {4}^{\textcolor{red}{1} \times \textcolor{b l u e}{6}} {r}^{\textcolor{red}{2} \times \textcolor{b l u e}{6}} {t}^{\textcolor{red}{1} \times \textcolor{b l u e}{6}} = {4}^{6} {r}^{12} {t}^{6} =$

$4096 {r}^{12} {t}^{6}$