Algebra Examples

$\frac{7 x^{\frac{3}{2}}}{- 14 x^{\frac{1}{3}}}$

Step 1

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

$\frac{7 x^{\frac{3}{2}} x^{- \frac{1}{3}}}{- 14}$

Step 2

Multiply $x^{\frac{3}{2}}$ by $x^{- \frac{1}{3}}$ by adding the exponents.

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Step 2.1

Move $x^{- \frac{1}{3}}$ .

$\frac{7 (x^{- \frac{1}{3}} x^{\frac{3}{2}})}{- 14}$

Step 2.2

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

$\frac{7 x^{- \frac{1}{3} + \frac{3}{2}}}{- 14}$

Step 2.3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 x^{- \frac{1}{3} \cdot \frac{2}{2} + \frac{3}{2}}}{- 14}$

Step 2.4

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

$\frac{7 x^{- \frac{1}{3} \cdot \frac{2}{2} + \frac{3}{2} \cdot \frac{3}{3}}}{- 14}$

Step 2.5

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

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Step 2.5.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{7 x^{- \frac{2}{3 \cdot 2} + \frac{3}{2} \cdot \frac{3}{3}}}{- 14}$

Step 2.5.2

Multiply $3$ by $2$ .

$\frac{7 x^{- \frac{2}{6} + \frac{3}{2} \cdot \frac{3}{3}}}{- 14}$

Step 2.5.3

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

$\frac{7 x^{- \frac{2}{6} + \frac{3 \cdot 3}{2 \cdot 3}}}{- 14}$

Step 2.5.4

Multiply $2$ by $3$ .

$\frac{7 x^{- \frac{2}{6} + \frac{3 \cdot 3}{6}}}{- 14}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{7 x^{\frac{- 2 + 3 \cdot 3}{6}}}{- 14}$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $3$ by $3$ .

$\frac{7 x^{\frac{- 2 + 9}{6}}}{- 14}$

Step 2.7.2

Add $- 2$ and $9$ .

$\frac{7 x^{\frac{7}{6}}}{- 14}$

Step 3

Factor $7$ out of $7 x^{\frac{7}{6}}$ .

$\frac{7 (x^{\frac{7}{6}})}{- 14}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $7$ out of $- 14$ .

$\frac{7 x^{\frac{7}{6}}}{7 \cdot - 2}$

Step 4.2

Cancel the common factor.

$\frac{7 x^{\frac{7}{6}}}{7 \cdot - 2}$

Step 4.3

Rewrite the expression.

$\frac{x^{\frac{7}{6}}}{- 2}$

Step 5

Move the negative in front of the fraction.

$- \frac{x^{\frac{7}{6}}}{2}$