Simplify (2a^3b)^3(-2b^4)

${(2 a^{3} b)}^{3} (- 2 b^{4})$

Rewrite using the commutative property of multiplication.

$- 2 {(2 a^{3} b)}^{3} b^{4}$

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

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

$- 2 ({(2 a^{3})}^{3} b^{3}) b^{4}$

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

$- 2 (2^{3} {(a^{3})}^{3} b^{3}) b^{4}$

Multiply $b^{3}$ by $b^{4}$ by adding the exponents.

Move $b^{4}$ .

$- 2 (2^{3} {(a^{3})}^{3} (b^{4} b^{3}))$

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

$- 2 (2^{3} {(a^{3})}^{3} b^{4 + 3})$

Add $4$ and $3$ .

$- 2 (2^{3} {(a^{3})}^{3} b^{7})$

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

$- 2 (8 {(a^{3})}^{3} b^{7})$

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

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

$- 2 (8 a^{3 \cdot 3} b^{7})$

Multiply $3$ by $3$ .

$- 2 (8 a^{9} b^{7})$

Multiply $8$ by $- 2$ .

$- 16 a^{9} b^{7}$