Algebra Examples

$\frac{27 a^{- 6} b^{4} c^{8}}{9 a^{2} b^{- 2} c^{8}}$

Step 1

Move $a^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{27 b^{4} c^{8}}{9 a^{2} b^{- 2} c^{8} a^{6}}$

Step 2

Multiply $a^{2}$ by $a^{6}$ by adding the exponents.

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Step 2.1

Move $a^{6}$ .

$\frac{27 b^{4} c^{8}}{9 (a^{6} a^{2}) b^{- 2} c^{8}}$

Step 2.2

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

$\frac{27 b^{4} c^{8}}{9 a^{6 + 2} b^{- 2} c^{8}}$

Step 2.3

Add $6$ and $2$ .

$\frac{27 b^{4} c^{8}}{9 a^{8} b^{- 2} c^{8}}$

Step 3

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

$\frac{27 b^{4} c^{8} b^{2}}{9 a^{8} c^{8}}$

Step 4

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

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Step 4.1

Move $b^{2}$ .

$\frac{27 (b^{2} b^{4}) c^{8}}{9 a^{8} c^{8}}$

Step 4.2

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

$\frac{27 b^{2 + 4} c^{8}}{9 a^{8} c^{8}}$

Step 4.3

Add $2$ and $4$ .

$\frac{27 b^{6} c^{8}}{9 a^{8} c^{8}}$

Step 5

Cancel the common factor of $27$ and $9$ .

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Step 5.1

Factor $9$ out of $27 b^{6} c^{8}$ .

$\frac{9 (3 b^{6} c^{8})}{9 a^{8} c^{8}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $9$ out of $9 a^{8} c^{8}$ .

$\frac{9 (3 b^{6} c^{8})}{9 (a^{8} c^{8})}$

Step 5.2.2

Cancel the common factor.

$\frac{9 (3 b^{6} c^{8})}{9 (a^{8} c^{8})}$

Step 5.2.3

Rewrite the expression.

$\frac{3 b^{6} c^{8}}{a^{8} c^{8}}$

Step 6

Cancel the common factor of $c^{8}$ .

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Step 6.1

Cancel the common factor.

$\frac{3 b^{6} c^{8}}{a^{8} c^{8}}$

Step 6.2

Rewrite the expression.

$\frac{3 b^{6}}{a^{8}}$