Algebra Examples

$(36 x^{\frac{5}{6}}) \div (4 x^{\frac{2}{3}})$

Step 1

Reduce the expression $(36 x^{\frac{5}{6}}) \div (4 x^{\frac{2}{3}})$ by cancelling the common factors.

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Step 1.1

Factor $4$ out of $36 x^{\frac{5}{6}}$ .

$4 (9 x^{\frac{5}{6}}) \div 4 x^{\frac{2}{3}}$

Step 1.2

Factor $4$ out of $4 x^{\frac{2}{3}}$ .

$4 (9 x^{\frac{5}{6}}) \div 4 (x^{\frac{2}{3}})$

Step 1.3

Cancel the common factor.

$4 (9 x^{\frac{5}{6}}) \div 4 x^{\frac{2}{3}}$

Step 1.4

Rewrite the expression.

$\frac{9 x^{\frac{5}{6}}}{x^{\frac{2}{3}}}$

Step 2

Move $x^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$9 x^{\frac{5}{6}} x^{- \frac{2}{3}}$

Step 3

Multiply $x^{\frac{5}{6}}$ by $x^{- \frac{2}{3}}$ by adding the exponents.

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Step 3.1

Move $x^{- \frac{2}{3}}$ .

$9 (x^{- \frac{2}{3}} x^{\frac{5}{6}})$

Step 3.2

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

$9 x^{- \frac{2}{3} + \frac{5}{6}}$

Step 3.3

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

$9 x^{- \frac{2}{3} \cdot \frac{2}{2} + \frac{5}{6}}$

Step 3.4

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

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Step 3.4.1

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

$9 x^{- \frac{2 \cdot 2}{3 \cdot 2} + \frac{5}{6}}$

Step 3.4.2

Multiply $3$ by $2$ .

$9 x^{- \frac{2 \cdot 2}{6} + \frac{5}{6}}$

Step 3.5

Combine the numerators over the common denominator.

$9 x^{\frac{- 2 \cdot 2 + 5}{6}}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 2$ by $2$ .

$9 x^{\frac{- 4 + 5}{6}}$

Step 3.6.2

Add $- 4$ and $5$ .

$9 x^{\frac{1}{6}}$

Step 4

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

$9 \sqrt[6]{x^{1}}$

Step 5

Anything raised to $1$ is the base itself.

$9 \sqrt[6]{x}$