Simplify (-6a^4b^3)^2*-2ab^5

${(- 6 a^{4} b^{3})}^{2} \cdot - 2 a b^{5}$

Rewrite using the commutative property of multiplication.

$- 2 {(- 6 a^{4} b^{3})}^{2} a b^{5}$

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

Apply the product rule to $- 6 a^{4} b^{3}$ .

$- 2 ({(- 6 a^{4})}^{2} {(b^{3})}^{2}) a b^{5}$

Apply the product rule to $- 6 a^{4}$ .

$- 2 ({(- 6)}^{2} {(a^{4})}^{2} {(b^{3})}^{2}) a b^{5}$

Raise $- 6$ to the power of $2$ .

$- 2 (36 {(a^{4})}^{2} {(b^{3})}^{2}) a b^{5}$

Multiply the exponents in ${(a^{4})}^{2}$ .

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

$- 2 (36 a^{4 \cdot 2} {(b^{3})}^{2}) a b^{5}$

Multiply $4$ by $2$ .

$- 2 (36 a^{8} {(b^{3})}^{2}) a b^{5}$

Multiply $a^{8}$ by $a$ by adding the exponents.

Move $a$ .

$- 2 (36 (a \cdot a^{8}) {(b^{3})}^{2}) b^{5}$

Multiply $a$ by $a^{8}$ .

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

$- 2 (36 (a^{1} a^{8}) {(b^{3})}^{2}) b^{5}$

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

$- 2 (36 a^{1 + 8} {(b^{3})}^{2}) b^{5}$

Add $1$ and $8$ .

$- 2 (36 a^{9} {(b^{3})}^{2}) b^{5}$

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

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

$- 2 (36 a^{9} b^{3 \cdot 2}) b^{5}$

Multiply $3$ by $2$ .

$- 2 (36 a^{9} b^{6}) b^{5}$

Multiply $b^{6}$ by $b^{5}$ by adding the exponents.

Move $b^{5}$ .

$- 2 (36 a^{9} (b^{5} b^{6}))$

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

$- 2 (36 a^{9} b^{5 + 6})$

Add $5$ and $6$ .

$- 2 (36 a^{9} b^{11})$

Multiply $36$ by $- 2$ .

$- 72 a^{9} b^{11}$