Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

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Step 2.1

Apply the product rule to $- 2 a b$ .

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

Step 2.2

Apply the product rule to $- 2 a$ .

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

Step 3

Multiply $a^{3}$ by $a^{2}$ by adding the exponents.

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Step 3.1

Move $a^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add $2$ and $3$ .

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

Step 4

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

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Step 4.1

Move $b$ .

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.3

Add $1$ and $3$ .

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

Step 5

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

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

Step 6

Multiply $- 8$ by $- 1$ .

$8 a^{5} b^{4}$