Basic Math Examples

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

Step 1

Rewrite the division as a fraction.

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

Step 2

Move ${(- a b^{2} c)}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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Step 3.1.1

Move $a$ .

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

Step 3.1.2

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

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.3

Add $1$ and $2$ .

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

Step 3.2

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

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Step 3.2.1

Move $b^{2}$ .

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

Step 3.2.2

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

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

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

Step 3.2.3

Add $2$ and $1$ .

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

Step 3.3

Multiply $c^{- 1}$ by $c$ by adding the exponents.

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Step 3.3.1

Move $c$ .

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

Step 3.3.2

Multiply $c$ by $c^{- 1}$ .

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Step 3.3.2.1

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

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

Step 3.3.2.2

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

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

Step 3.3.3

Subtract $1$ from $1$ .

$\frac{1}{a^{3} b^{3} c^{0} \cdot - 1}$

Step 3.4

Simplify $a^{3} b^{3} c^{0} \cdot - 1$ .

$\frac{1}{a^{3} b^{3} \cdot - 1}$

Step 4

Cancel the common factor of $1$ and $- 1$ .

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Step 4.1

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 4.2

Move the negative in front of the fraction.

$- \frac{1}{a^{3} b^{3}}$