Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

$\frac{a^{3}}{a b^{3} b^{2} c}$

Step 3

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

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Step 3.1

Move $b^{2}$ .

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

Step 3.2

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

$\frac{a^{3}}{a b^{2 + 3} c}$

Step 3.3

Add $2$ and $3$ .

$\frac{a^{3}}{a b^{5} c}$

Step 4

Cancel the common factor of $a^{3}$ and $a$ .

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Step 4.1

Factor $a$ out of $a^{3}$ .

$\frac{a \cdot a^{2}}{a b^{5} c}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a$ out of $a b^{5} c$ .

$\frac{a \cdot a^{2}}{a (b^{5} c)}$

Step 4.2.2

Cancel the common factor.

$\frac{a \cdot a^{2}}{a (b^{5} c)}$

Step 4.2.3

Rewrite the expression.

$\frac{a^{2}}{b^{5} c}$