Simplify 3x^2(3xy^3)^2

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

Step 1

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

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

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

Apply the product rule to $3 x$ .

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

Step 2

Multiply $3$ by $3^{2}$ by adding the exponents.

Move $3^{2}$ .

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

Multiply $3^{2}$ by $3$ .

Raise $3$ to the power of $1$ .

$3^{2} \cdot 3^{1} x^{2} (x^{2} {(y^{3})}^{2})$

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

$3^{2 + 1} x^{2} (x^{2} {(y^{3})}^{2})$

Add $2$ and $1$ .

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

Step 3

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

$3^{3} x^{4} {(y^{3})}^{2}$

Step 4

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

$27 x^{4} {(y^{3})}^{2}$

Step 5

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

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

$27 x^{4} y^{3 \cdot 2}$

Multiply $3$ by $2$ .

$27 x^{4} y^{6}$