Basic Math Examples

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6}} f^{\frac{5}{6}})}{\frac{5}{6} \cdot (c^{\frac{1}{6} - 1} f^{- \frac{1}{6}})}$

Step 1

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

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6}} f^{\frac{5}{6}}) f^{\frac{1}{6}}}{\frac{5}{6} \cdot c^{\frac{1}{6} - 1}}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $f^{\frac{5}{6}}$ by $f^{\frac{1}{6}}$ by adding the exponents.

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Step 2.1.1

Move $f^{\frac{1}{6}}$ .

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6}} (f^{\frac{1}{6}} f^{\frac{5}{6}}))}{\frac{5}{6} \cdot c^{\frac{1}{6} - 1}}$

Step 2.1.2

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

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6}} f^{\frac{1}{6} + \frac{5}{6}})}{\frac{5}{6} \cdot c^{\frac{1}{6} - 1}}$

Step 2.1.3

Combine the numerators over the common denominator.

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6}} f^{\frac{1 + 5}{6}})}{\frac{5}{6} \cdot c^{\frac{1}{6} - 1}}$

Step 2.1.4

Add $1$ and $5$ .

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6}} f^{\frac{6}{6}})}{\frac{5}{6} \cdot c^{\frac{1}{6} - 1}}$

Step 2.1.5

Divide $6$ by $6$ .

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6}} f^{1})}{\frac{5}{6} \cdot c^{\frac{1}{6} - 1}}$

Step 2.2

Simplify $\frac{1}{6} \cdot (c^{- \frac{5}{6}} f^{1})$ .

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6}} f)}{\frac{5}{6} \cdot c^{\frac{1}{6} - 1}}$

Step 3

Cancel the common factor of $c^{- \frac{5}{6}}$ and $c^{\frac{1}{6} - 1}$ .

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Step 3.1

Factor $c^{\frac{1}{6} - 1}$ out of $\frac{1}{6} \cdot (c^{- \frac{5}{6}} f)$ .

$\frac{c^{\frac{1}{6} - 1} (\frac{1}{6} \cdot (c^{- \frac{5}{6} - (\frac{1}{6} - 1)} f))}{\frac{5}{6} \cdot c^{\frac{1}{6} - 1}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $c^{\frac{1}{6} - 1}$ out of $\frac{5}{6} \cdot c^{\frac{1}{6} - 1}$ .

$\frac{c^{\frac{1}{6} - 1} (\frac{1}{6} \cdot (c^{- \frac{5}{6} - (\frac{1}{6} - 1)} f))}{c^{\frac{1}{6} - 1} \cdot \frac{5}{6}}$

Step 3.2.2

Cancel the common factor.

$\frac{c^{\frac{1}{6} - 1} (\frac{1}{6} \cdot (c^{- \frac{5}{6} - (\frac{1}{6} - 1)} f))}{c^{\frac{1}{6} - 1} \cdot \frac{5}{6}}$

Step 3.2.3

Rewrite the expression.

$\frac{\frac{1}{6} \cdot (c^{- \frac{5}{6} - (\frac{1}{6} - 1)} f)}{\frac{5}{6}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{6} \cdot c^{- \frac{5}{6} - (\frac{1}{6} - 1)} f \frac{6}{5}$

Step 5

Simplify each term.

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Step 5.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{1}{6} \cdot c^{- \frac{5}{6} - (\frac{1}{6} - 1 \cdot \frac{6}{6})} f \frac{6}{5}$

Step 5.2

Combine $- 1$ and $\frac{6}{6}$ .

$\frac{1}{6} \cdot c^{- \frac{5}{6} - (\frac{1}{6} + \frac{- 1 \cdot 6}{6})} f \frac{6}{5}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{1}{6} \cdot c^{- \frac{5}{6} - \frac{1 - 1 \cdot 6}{6}} f \frac{6}{5}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply $- 1$ by $6$ .

$\frac{1}{6} \cdot c^{- \frac{5}{6} - \frac{1 - 6}{6}} f \frac{6}{5}$

Step 5.4.2

Subtract $6$ from $1$ .

$\frac{1}{6} \cdot c^{- \frac{5}{6} - \frac{- 5}{6}} f \frac{6}{5}$

Step 5.5

Move the negative in front of the fraction.

$\frac{1}{6} \cdot c^{- \frac{5}{6} - - \frac{5}{6}} f \frac{6}{5}$

Step 5.6

Multiply $- - \frac{5}{6}$ .

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Step 5.6.1

Multiply $- 1$ by $- 1$ .

$\frac{1}{6} \cdot c^{- \frac{5}{6} + 1 (\frac{5}{6})} f \frac{6}{5}$

Step 5.6.2

Multiply $\frac{5}{6}$ by $1$ .

$\frac{1}{6} \cdot c^{- \frac{5}{6} + \frac{5}{6}} f \frac{6}{5}$

Step 6

Simplify terms.

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Step 6.1

Combine the numerators over the common denominator.

$\frac{1}{6} \cdot c^{\frac{- 5 + 5}{6}} f \frac{6}{5}$

Step 6.2

Simplify the expression.

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Step 6.2.1

Add $- 5$ and $5$ .

$\frac{1}{6} \cdot c^{\frac{0}{6}} f \frac{6}{5}$

Step 6.2.2

Divide $0$ by $6$ .

$\frac{1}{6} \cdot c^{0} f \frac{6}{5}$

Step 6.2.3

Anything raised to $0$ is $1$ .

$\frac{1}{6} \cdot 1 f \frac{6}{5}$

Step 6.2.4

Multiply $\frac{1}{6}$ by $1$ .

$\frac{1}{6} f \frac{6}{5}$

Step 6.3

Combine $\frac{1}{6}$ and $f$ .

$\frac{f}{6} \cdot \frac{6}{5}$

Step 6.4

Cancel the common factor of $6$ .

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Step 6.4.1

Cancel the common factor.

$\frac{f}{6} \cdot \frac{6}{5}$

Step 6.4.2

Rewrite the expression.

$f \frac{1}{5}$

Step 6.5

Combine $f$ and $\frac{1}{5}$ .

$\frac{f}{5}$