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

Oct 24, 2017

$27 {a}^{12} {b}^{6}$

#### Explanation:

Move the $3$ inside by simply multiplying every power by $3$.

${\left(3 {a}^{4} {b}^{2}\right)}^{3} = {\left({3}^{1} {a}^{4} {b}^{2}\right)}^{3}$

$= \left({3}^{1 \times 3} {a}^{4 \times 3} {b}^{2 \times 3}\right)$

$= {3}^{3} {a}^{12} {b}^{6}$

You can calculate ${3}^{3}$ straight away, because

${3}^{3} = 3 \times 3 \times 3 = \left(3 \times 3\right) \times 3 = 9 \times 3 = 27$

so

${\left(3 {a}^{4} {b}^{2}\right)}^{3} = 27 {a}^{12} {b}^{6}$