Divide (x^(3/5))/(x^(1/4))

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

Step 1

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

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

Step 2

Multiply $x^{\frac{3}{5}}$ by $x^{- \frac{1}{4}}$ by adding the exponents.

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

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

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

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

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{5}$ by $\frac{4}{4}$ .

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

Multiply $5$ by $4$ .

$x^{\frac{3 \cdot 4}{20} - \frac{1}{4} \cdot \frac{5}{5}}$

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$x^{\frac{3 \cdot 4}{20} - \frac{5}{4 \cdot 5}}$

Multiply $4$ by $5$ .

$x^{\frac{3 \cdot 4}{20} - \frac{5}{20}}$

Combine the numerators over the common denominator.

$x^{\frac{3 \cdot 4 - 5}{20}}$

Simplify the numerator.

Multiply $3$ by $4$ .

$x^{\frac{12 - 5}{20}}$

Subtract $5$ from $12$ .

$x^{\frac{7}{20}}$