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

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

Rewrite using the commutative property of multiplication.

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

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

Apply the product rule to $3 x^{2} y$ .

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

Apply the product rule to $3 x^{2}$ .

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

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

Move $y$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

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

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

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

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

Multiply $2$ by $3$ .

$2 (27 x^{6} y^{4}) x$

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

Move $x$ .

$2 (27 (x \cdot x^{6}) y^{4})$

Multiply $x$ by $x^{6}$ .

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

$2 (27 (x^{1} x^{6}) y^{4})$

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

$2 (27 x^{1 + 6} y^{4})$

Add $1$ and $6$ .

$2 (27 x^{7} y^{4})$

Multiply $27$ by $2$ .

$54 x^{7} y^{4}$