Simplify 2xy(3xy)^4

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

Step 1

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

Apply the product rule to $3 x y$ .

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

Apply the product rule to $3 x$ .

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

Step 2

Multiply $x$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

Multiply $x^{4}$ by $x$ .

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

$2 (x^{4} x^{1}) y (3^{4} y^{4})$

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

$2 x^{4 + 1} y (3^{4} y^{4})$

Add $4$ and $1$ .

$2 x^{5} y (3^{4} y^{4})$

Step 3

Multiply $y$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$2 x^{5} (y^{4} y) \cdot 3^{4}$

Multiply $y^{4}$ by $y$ .

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

$2 x^{5} (y^{4} y^{1}) \cdot 3^{4}$

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

$2 x^{5} y^{4 + 1} \cdot 3^{4}$

Add $4$ and $1$ .

$2 x^{5} y^{5} \cdot 3^{4}$

Step 4

Raise $3$ to the power of $4$ .

$2 x^{5} y^{5} \cdot 81$

Step 5

Multiply $81$ by $2$ .

$162 x^{5} y^{5}$