How do you simplify [(2xy^3)^2]^3?

Jan 19, 2017

${\left[{\left(2 x {y}^{3}\right)}^{2}\right]}^{3} = 64 {x}^{6} {y}^{18}$

Explanation:

We will use the following properties of exponents:

• ${\left({x}^{a}\right)}^{b} = {x}^{a b}$
• ${\left(x y\right)}^{a} = {x}^{a} {y}^{a}$

With those,

${\left[{\left(2 x {y}^{3}\right)}^{2}\right]}^{3} = {\left(2 x {y}^{3}\right)}^{2 \cdot 3}$

$= {\left(2 x {y}^{3}\right)}^{6}$

$= {2}^{6} {x}^{6} {\left({y}^{3}\right)}^{6}$

$= {2}^{6} {x}^{6} {y}^{3 \cdot 6}$

$= {2}^{6} {x}^{6} {y}^{18}$

$= 64 {x}^{6} {y}^{18}$