Algebra Examples

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

Step 1

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

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Step 1.1

Move $a^{2}$ .

$- (a^{2} a) b (- b^{2} c^{2}) (- 1 b^{2})$

Step 1.2

Multiply $a^{2}$ by $a$ .

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Step 1.2.1

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

$- (a^{2} a^{1}) b (- b^{2} c^{2}) (- 1 b^{2})$

Step 1.2.2

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

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

Step 1.3

Add $2$ and $1$ .

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

Step 2

Multiply $b$ by $b^{2}$ by adding the exponents.

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Step 2.1

Move $b^{2}$ .

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

Step 2.2

Multiply $b^{2}$ by $b$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $2$ and $1$ .

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

Step 3

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

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Step 3.1

Move $b^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add $2$ and $3$ .

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

Step 4

Rewrite $- 1 c^{2}$ as $- c^{2}$ .

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

Step 5

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

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Step 5.1

Multiply $- 1$ by $- 1$ .

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

Step 5.2

Multiply $a^{3}$ by $1$ .

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

Step 6

Move $- 1$ to the left of $a^{3} b^{5} c^{2}$ .

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

Step 7

Rewrite $- 1 (a^{3} b^{5} c^{2})$ as $- (a^{3} b^{5} c^{2})$ .

$- a^{3} b^{5} c^{2}$