Simplify (3xy)^2*(-4x^3y^2)^3

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

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

Apply the product rule to $3 x y$ .

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

Apply the product rule to $3 x$ .

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

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

$9 x^{2} y^{2} \cdot {(- 4 x^{3} y^{2})}^{3}$

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

Apply the product rule to $- 4 x^{3} y^{2}$ .

$9 x^{2} y^{2} \cdot ({(- 4 x^{3})}^{3} {(y^{2})}^{3})$

Apply the product rule to $- 4 x^{3}$ .

$9 x^{2} y^{2} \cdot ({(- 4)}^{3} {(x^{3})}^{3} {(y^{2})}^{3})$

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

$9 x^{2} y^{2} \cdot (- 64 {(x^{3})}^{3} {(y^{2})}^{3})$

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

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

$9 x^{2} y^{2} \cdot (- 64 x^{3 \cdot 3} {(y^{2})}^{3})$

Multiply $3$ by $3$ .

$9 x^{2} y^{2} \cdot (- 64 x^{9} {(y^{2})}^{3})$

Multiply $x^{2}$ by $x^{9}$ by adding the exponents.

Move $x^{9}$ .

$9 (x^{9} x^{2}) y^{2} \cdot (- 64 {(y^{2})}^{3})$

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

$9 x^{9 + 2} y^{2} \cdot (- 64 {(y^{2})}^{3})$

Add $9$ and $2$ .

$9 x^{11} y^{2} \cdot (- 64 {(y^{2})}^{3})$

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

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

$9 x^{11} y^{2} \cdot (- 64 y^{2 \cdot 3})$

Multiply $2$ by $3$ .

$9 x^{11} y^{2} \cdot (- 64 y^{6})$

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

Move $y^{6}$ .

$9 x^{11} (y^{6} y^{2}) \cdot - 64$

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

$9 x^{11} y^{6 + 2} \cdot - 64$

Add $6$ and $2$ .

$9 x^{11} y^{8} \cdot - 64$

Multiply $- 64$ by $9$ .

$- 576 x^{11} y^{8}$