Pre-Algebra Examples

$\frac{27 a^{3} b^{- 2} c^{- 2}}{3 a^{2} b^{- 4} c^{- 2}}$

Step 1

Move $b^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{27 a^{3} b^{- 2} c^{- 2} b^{4}}{3 a^{2} c^{- 2}}$

Step 2

Multiply $b^{- 2}$ by $b^{4}$ by adding the exponents.

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Step 2.1

Move $b^{4}$ .

$\frac{27 a^{3} (b^{4} b^{- 2}) c^{- 2}}{3 a^{2} c^{- 2}}$

Step 2.2

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

$\frac{27 a^{3} b^{4 - 2} c^{- 2}}{3 a^{2} c^{- 2}}$

Step 2.3

Subtract $2$ from $4$ .

$\frac{27 a^{3} b^{2} c^{- 2}}{3 a^{2} c^{- 2}}$

Step 3

Cancel the common factor of $27$ and $3$ .

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Step 3.1

Factor $3$ out of $27 a^{3} b^{2} c^{- 2}$ .

$\frac{3 (9 a^{3} b^{2} c^{- 2})}{3 a^{2} c^{- 2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3 a^{2} c^{- 2}$ .

$\frac{3 (9 a^{3} b^{2} c^{- 2})}{3 (a^{2} c^{- 2})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (9 a^{3} b^{2} c^{- 2})}{3 (a^{2} c^{- 2})}$

Step 3.2.3

Rewrite the expression.

$\frac{9 a^{3} b^{2} c^{- 2}}{a^{2} c^{- 2}}$

Step 4

Cancel the common factor of $a^{3}$ and $a^{2}$ .

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Step 4.1

Factor $a^{2}$ out of $9 a^{3} b^{2} c^{- 2}$ .

$\frac{a^{2} (9 a b^{2} c^{- 2})}{a^{2} c^{- 2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{2}$ out of $a^{2} c^{- 2}$ .

$\frac{a^{2} (9 a b^{2} c^{- 2})}{a^{2} (c^{- 2})}$

Step 4.2.2

Cancel the common factor.

$\frac{a^{2} (9 a b^{2} c^{- 2})}{a^{2} c^{- 2}}$

Step 4.2.3

Rewrite the expression.

$\frac{9 a b^{2} c^{- 2}}{c^{- 2}}$

Step 5

Cancel the common factor of $c^{- 2}$ .

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Step 5.1

Cancel the common factor.

$\frac{9 a b^{2} c^{- 2}}{c^{- 2}}$

Step 5.2

Divide $9 a b^{2}$ by $1$ .

$9 a b^{2}$