Simplify (-2a^5b^3)^4

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

Step 1

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

Apply the product rule to $- 2 a^{5} b^{3}$ .

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

Apply the product rule to $- 2 a^{5}$ .

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

Step 2

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

$16 {(a^{5})}^{4} {(b^{3})}^{4}$

Step 3

Multiply the exponents in ${(a^{5})}^{4}$ .

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

$16 a^{5 \cdot 4} {(b^{3})}^{4}$

Multiply $5$ by $4$ .

$16 a^{20} {(b^{3})}^{4}$

Step 4

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

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

$16 a^{20} b^{3 \cdot 4}$

Multiply $3$ by $4$ .

$16 a^{20} b^{12}$