Simplify (x^(1/3))/(x^(-3/4)x^(1/4))

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

Step 1

Multiply $x^{- \frac{3}{4}}$ by $x^{\frac{1}{4}}$ by adding the exponents.

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

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

Combine the numerators over the common denominator.

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

Add $- 3$ and $1$ .

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

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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

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

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

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

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

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

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

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

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

Multiply $3$ by $2$ .

$x^{\frac{2}{6} + \frac{1}{2} \cdot \frac{3}{3}}$

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

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

Multiply $2$ by $3$ .

$x^{\frac{2}{6} + \frac{3}{6}}$

Combine the numerators over the common denominator.

$x^{\frac{2 + 3}{6}}$

Add $2$ and $3$ .

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