# How do you simplify (2ag^2)^4(3a^2g^3)^2?

Jun 15, 2018

$144 {a}^{8} {g}^{14}$

#### Explanation:

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

First, let's look at ${\left(2 a {g}^{2}\right)}^{4}$. The exponent $4$ applies to everything inside the parenthesis, so:
${2}^{4} = 16$

${a}^{4} = {a}^{4}$

${\left({g}^{2}\right)}^{4} = {g}^{2 \cdot 4} = {g}^{8}$

Multiply them all together:
$16 {a}^{4} {g}^{8}$

Now ${\left(3 {a}^{2} {g}^{3}\right)}^{2}$:
${3}^{2} = 9$

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

${\left({g}^{3}\right)}^{2} = {g}^{3 \cdot 2} = {g}^{6}$

Multiply them all together:
$9 {a}^{4} {g}^{6}$

Now multiply both simplified expressions:
$\left(16 {a}^{4} {g}^{8}\right) \left(9 {a}^{4} {g}^{6}\right)$

Simplify:
$144 {a}^{4 + 4} {g}^{8 + 6}$

Therefore, the simplified expression is:
$144 {a}^{8} {g}^{14}$

Hope this helps!