# How do you simplify (3xy^3)^2(xy)^6?

May 4, 2018

$9 {x}^{8} {y}^{12}$

#### Explanation:

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

This can also be written (for simplicity of understanding) as:

${\left({3}^{1} {x}^{1} {y}^{3}\right)}^{2} {\left({x}^{1} {y}^{1}\right)}^{6}$

We first open the brackets separately and simplify them by multiplying the exponential power outside the bracket with each individual power inside the bracket.

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

Since ${3}^{2}$ is $9$ we write that:

$\left(9 {x}^{2} {y}^{6}\right) \left({x}^{6} {y}^{6}\right)$

Now we combine both brackets by opening them and multiplying the like terms with each other by adding their respective powers:

$9 {x}^{8} {y}^{12}$

May 4, 2018

(3xy^3)^2(xy)^6=color(blue)(9x^8y^12

#### Explanation:

Simplify:

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

Apply multiplication distributive property: ${\left(a b\right)}^{m} = {a}^{m} {b}^{m}$

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

Apply power rule of exponents: ${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$

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

Simplify ${3}^{2}$ to $9$.

$9 {x}^{2} {y}^{3 \cdot 2} {x}^{6} {y}^{6}$

Simplify ${y}^{3 \cdot 2}$ to ${y}^{6}$.

$9 {x}^{2} {y}^{6} {x}^{6} {y}^{6}$

Regroup variables.

$9 {x}^{2} {x}^{6} {y}^{6} {y}^{6}$

Apply product rule of exponents: ${a}^{m} {a}^{n} = {a}^{m + n}$

$9 {x}^{2 + 6} {y}^{6 + 6}$

$9 {x}^{8} {y}^{12}$