Basic Math Examples

$\frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}$

Step 1

Move $x^{\frac{5}{6}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{4}{3}} x^{- \frac{5}{6}}$

Step 2

Multiply $x^{\frac{4}{3}}$ by $x^{- \frac{5}{6}}$ 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.

$x^{\frac{4}{3} - \frac{5}{6}}$

Step 2.2

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{4}{3} \cdot \frac{2}{2} - \frac{5}{6}}$

Step 2.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

$x^{\frac{4 \cdot 2}{3 \cdot 2} - \frac{5}{6}}$

Step 2.3.2

Multiply $3$ by $2$ .

$x^{\frac{4 \cdot 2}{6} - \frac{5}{6}}$

Step 2.4

Combine the numerators over the common denominator.

$x^{\frac{4 \cdot 2 - 5}{6}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $2$ .

$x^{\frac{8 - 5}{6}}$

Step 2.5.2

Subtract $5$ from $8$ .

$x^{\frac{3}{6}}$

Step 2.6

Cancel the common factor of $3$ and $6$ .

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Step 2.6.1

Factor $3$ out of $3$ .

$x^{\frac{3 (1)}{6}}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $3$ out of $6$ .

$x^{\frac{3 \cdot 1}{3 \cdot 2}}$

Step 2.6.2.2

Cancel the common factor.

$x^{\frac{3 \cdot 1}{3 \cdot 2}}$

Step 2.6.2.3

Rewrite the expression.

$x^{\frac{1}{2}}$