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

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

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

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

Raise $2$ to the power of $4$ .

$16 {(x^{3})}^{4} {(- 3 x^{2} y^{3})}^{2}$

Multiply the exponents in ${(x^{3})}^{4}$ .

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

$16 x^{3 \cdot 4} {(- 3 x^{2} y^{3})}^{2}$

Multiply $3$ by $4$ .

$16 x^{12} {(- 3 x^{2} y^{3})}^{2}$

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

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

$16 x^{12} ({(- 3 x^{2})}^{2} {(y^{3})}^{2})$

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

$16 x^{12} ({(- 3)}^{2} {(x^{2})}^{2} {(y^{3})}^{2})$

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

$16 x^{12} (9 {(x^{2})}^{2} {(y^{3})}^{2})$

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

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

$16 x^{12} (9 x^{2 \cdot 2} {(y^{3})}^{2})$

Multiply $2$ by $2$ .

$16 x^{12} (9 x^{4} {(y^{3})}^{2})$

Multiply $x^{12}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$16 (x^{4} x^{12}) (9 {(y^{3})}^{2})$

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

$16 x^{4 + 12} (9 {(y^{3})}^{2})$

Add $4$ and $12$ .

$16 x^{16} (9 {(y^{3})}^{2})$

Rewrite using the commutative property of multiplication.

$16 \cdot 9 x^{16} {(y^{3})}^{2}$

Multiply $16$ by $9$ .

$144 x^{16} {(y^{3})}^{2}$

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

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

$144 x^{16} y^{3 \cdot 2}$

Multiply $3$ by $2$ .

$144 x^{16} y^{6}$