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

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

Rewrite using the commutative property of multiplication.

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

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

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

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

Apply the product rule to $3 x$ .

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

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

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

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

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

Multiply $3$ by $3$ .

$2 (27 x^{4} y^{9})$

Multiply $27$ by $2$ .

$54 x^{4} y^{9}$