Precalculus Examples

$\frac{6 x^{- \frac{4}{3}} + 2 x^{\frac{5}{3}}}{2 x^{- \frac{1}{3}}}$

Step 1

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

$\frac{(6 x^{- \frac{4}{3}} + 2 x^{\frac{5}{3}}) x^{\frac{1}{3}}}{2}$

Step 2

Factor $2$ out of $(6 x^{- \frac{4}{3}} + 2 x^{\frac{5}{3}}) x^{\frac{1}{3}}$ .

$\frac{2 ((3 x^{- \frac{4}{3}} + x^{\frac{5}{3}}) x^{\frac{1}{3}})}{2}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $2$ out of $2$ .

$\frac{2 ((3 x^{- \frac{4}{3}} + x^{\frac{5}{3}}) x^{\frac{1}{3}})}{2 (1)}$

Step 3.2

Cancel the common factor.

$\frac{2 ((3 x^{- \frac{4}{3}} + x^{\frac{5}{3}}) x^{\frac{1}{3}})}{2 \cdot 1}$

Step 3.3

Rewrite the expression.

$\frac{(3 x^{- \frac{4}{3}} + x^{\frac{5}{3}}) x^{\frac{1}{3}}}{1}$

Step 3.4

Divide $(3 x^{- \frac{4}{3}} + x^{\frac{5}{3}}) x^{\frac{1}{3}}$ by $1$ .

$(3 x^{- \frac{4}{3}} + x^{\frac{5}{3}}) x^{\frac{1}{3}}$

Step 4

Simplify each term.

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Step 4.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(3 \frac{1}{x^{\frac{4}{3}}} + x^{\frac{5}{3}}) x^{\frac{1}{3}}$

Step 4.2

Combine $3$ and $\frac{1}{x^{\frac{4}{3}}}$ .

$(\frac{3}{x^{\frac{4}{3}}} + x^{\frac{5}{3}}) x^{\frac{1}{3}}$

Step 5

To write $x^{\frac{5}{3}}$ as a fraction with a common denominator, multiply by $\frac{x^{\frac{4}{3}}}{x^{\frac{4}{3}}}$ .

$(\frac{3}{x^{\frac{4}{3}}} + \frac{x^{\frac{5}{3}} x^{\frac{4}{3}}}{x^{\frac{4}{3}}}) x^{\frac{1}{3}}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 + x^{\frac{5}{3}} x^{\frac{4}{3}}}{x^{\frac{4}{3}}} x^{\frac{1}{3}}$

Step 7

Multiply $x^{\frac{5}{3}}$ by $x^{\frac{4}{3}}$ by adding the exponents.

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Step 7.1

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

$\frac{3 + x^{\frac{5}{3} + \frac{4}{3}}}{x^{\frac{4}{3}}} x^{\frac{1}{3}}$

Step 7.2

Combine the numerators over the common denominator.

$\frac{3 + x^{\frac{5 + 4}{3}}}{x^{\frac{4}{3}}} x^{\frac{1}{3}}$

Step 7.3

Add $5$ and $4$ .

$\frac{3 + x^{\frac{9}{3}}}{x^{\frac{4}{3}}} x^{\frac{1}{3}}$

Step 7.4

Divide $9$ by $3$ .

$\frac{3 + x^{3}}{x^{\frac{4}{3}}} x^{\frac{1}{3}}$

Step 8

Cancel the common factor of $x^{\frac{1}{3}}$ .

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Step 8.1

Factor $x^{\frac{1}{3}}$ out of $x^{\frac{4}{3}}$ .

$\frac{3 + x^{3}}{x^{\frac{1}{3}} x^{\frac{3}{3}}} x^{\frac{1}{3}}$

Step 8.2

Cancel the common factor.

$\frac{3 + x^{3}}{x^{\frac{1}{3}} x^{\frac{3}{3}}} x^{\frac{1}{3}}$

Step 8.3

Rewrite the expression.

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

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Cancel the common factor.

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

Step 9.2

Rewrite the expression.

$\frac{3 + x^{3}}{x^{1}}$

Step 10

Simplify.

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