Simplify (3xy^3)^2(xy)^6

${(3 x y^{3})}^{2} {(x y)}^{6}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $3 x y^{3}$ .

${(3 x)}^{2} {(y^{3})}^{2} {(x y)}^{6}$

Apply the product rule to $3 x$ .

$3^{2} x^{2} {(y^{3})}^{2} {(x y)}^{6}$

Step 2

Raise $3$ to the power of $2$ .

$9 x^{2} {(y^{3})}^{2} {(x y)}^{6}$

Step 3

Multiply the exponents in ${(y^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $3$ by $2$ .

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

Step 4

Apply the product rule to $x y$ .

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

Step 5

Multiply $x^{2}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $6$ and $2$ .

$9 x^{8} y^{6} y^{6}$

Step 6

Multiply $y^{6}$ by $y^{6}$ by adding the exponents.

Move $y^{6}$ .

$9 x^{8} (y^{6} y^{6})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$9 x^{8} y^{6 + 6}$

Add $6$ and $6$ .

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