Simplify (x^(5/4)x^(-1/4))/(x^(1/3))

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

Step 1

Multiply $x^{\frac{5}{4}}$ by $x^{- \frac{1}{4}}$ by adding the exponents.

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $5$ .

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

Divide $4$ by $4$ .

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

Step 2

Simplify $x^{1}$ .

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

Step 3

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

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

Step 4

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

Multiply $x$ by $x^{- \frac{1}{3}}$ .

Raise $x$ to the power of $1$ .

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

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

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $3$ .

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