# How do you simplify (16a^4)^(3/2)?

Feb 29, 2016

$64 {a}^{6}$

#### Explanation:

To simplify ${\left(16 {a}^{4}\right)}^{\frac{3}{2}}$, remember the identity ${\left({a}^{m}\right)}^{n} = {a}^{m n}$ and ${\left(a b\right)}^{m} = {a}^{m} \times {b}^{m}$

Hence, ${\left(16 {a}^{4}\right)}^{\frac{3}{2}} = {16}^{\frac{3}{2}} \times {a}^{4 \times \left(\frac{3}{2}\right)}$, but $16 = {2}^{4}$

Hence this is ${\left({2}^{4}\right)}^{\frac{3}{2}} \times {a}^{6}$

or ${2}^{\left(4 \times \frac{3}{2}\right)} \times \left({a}^{6}\right)$

or ${2}^{6} \cdot {a}^{6} = 64 {a}^{6}$