Simplify (5ab)*(-2a^2b)^3

$(5 a b) \cdot {(- 2 a^{2} b)}^{3}$

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

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

$5 a b \cdot ({(- 2 a^{2})}^{3} b^{3})$

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

$5 a b \cdot ({(- 2)}^{3} {(a^{2})}^{3} b^{3})$

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

Move $b^{3}$ .

$5 a (b^{3} b) \cdot ({(- 2)}^{3} {(a^{2})}^{3})$

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

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

$5 a (b^{3} b^{1}) \cdot ({(- 2)}^{3} {(a^{2})}^{3})$

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

$5 a b^{3 + 1} \cdot ({(- 2)}^{3} {(a^{2})}^{3})$

Add $3$ and $1$ .

$5 a b^{4} \cdot ({(- 2)}^{3} {(a^{2})}^{3})$

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

$5 a b^{4} \cdot (- 8 {(a^{2})}^{3})$

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

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

$5 a b^{4} \cdot (- 8 a^{2 \cdot 3})$

Multiply $2$ by $3$ .

$5 a b^{4} \cdot (- 8 a^{6})$

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

Move $a^{6}$ .

$5 (a^{6} a) b^{4} \cdot - 8$

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

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

$5 (a^{6} a^{1}) b^{4} \cdot - 8$

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

$5 a^{6 + 1} b^{4} \cdot - 8$

Add $6$ and $1$ .

$5 a^{7} b^{4} \cdot - 8$

Multiply $- 8$ by $5$ .

$- 40 a^{7} b^{4}$