Divide (x^(5/8))/(x^(1/4))

$\frac{x^{\frac{5}{8}}}{x^{\frac{1}{4}}}$

Step 1

Move $x^{\frac{1}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{5}{8}} x^{- \frac{1}{4}}$

Step 2

Multiply $x^{\frac{5}{8}}$ by $x^{- \frac{1}{4}}$ by adding the exponents.

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

$x^{\frac{5}{8} - \frac{1}{4}}$

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{5}{8} - \frac{1}{4} \cdot \frac{2}{2}}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$x^{\frac{5}{8} - \frac{2}{4 \cdot 2}}$

Multiply $4$ by $2$ .

$x^{\frac{5}{8} - \frac{2}{8}}$

Combine the numerators over the common denominator.

$x^{\frac{5 - 2}{8}}$

Subtract $2$ from $5$ .

$x^{\frac{3}{8}}$