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

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Apply the product rule to $5 a^{4} b^{2}$ .

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

Apply the product rule to $5 a^{4}$ .

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

Step 3

Raise $5$ to the power of $3$ .

$- 2 (125 {(a^{4})}^{3} {(b^{2})}^{3}) b^{4}$

Step 4

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

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

$- 2 (125 a^{4 \cdot 3} {(b^{2})}^{3}) b^{4}$

Multiply $4$ by $3$ .

$- 2 (125 a^{12} {(b^{2})}^{3}) b^{4}$

Step 5

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

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

$- 2 (125 a^{12} b^{2 \cdot 3}) b^{4}$

Multiply $2$ by $3$ .

$- 2 (125 a^{12} b^{6}) b^{4}$

Step 6

Multiply $b^{6}$ by $b^{4}$ by adding the exponents.

Move $b^{4}$ .

$- 2 (125 a^{12} (b^{4} b^{6}))$

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

$- 2 (125 a^{12} b^{4 + 6})$

Add $4$ and $6$ .

$- 2 (125 a^{12} b^{10})$

Step 7

Multiply $125$ by $- 2$ .

$- 250 a^{12} b^{10}$