Algebra Examples

$\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}$

Step 1

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

$x^{\frac{5}{6}} x^{- \frac{1}{6}}$

Step 2

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

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Step 2.1

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

$x^{\frac{5}{6} - \frac{1}{6}}$

Step 2.2

Combine the numerators over the common denominator.

$x^{\frac{5 - 1}{6}}$

Step 2.3

Subtract $1$ from $5$ .

$x^{\frac{4}{6}}$

Step 2.4

Cancel the common factor of $4$ and $6$ .

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Step 2.4.1

Factor $2$ out of $4$ .

$x^{\frac{2 (2)}{6}}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $6$ .

$x^{\frac{2 \cdot 2}{2 \cdot 3}}$

Step 2.4.2.2

Cancel the common factor.

$x^{\frac{2 \cdot 2}{2 \cdot 3}}$

Step 2.4.2.3

Rewrite the expression.

$x^{\frac{2}{3}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[3]{x^{2}}$