Simplify (x^(3/2)y^(-1/4))/(x^(3/4)y^(3/4))

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

Step 1

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

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

Step 2

Simplify the denominator.

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

Move $y^{\frac{1}{4}}$ .

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

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

$\frac{x^{\frac{3}{2}}}{x^{\frac{3}{4}} y^{\frac{1}{4} + \frac{3}{4}}}$

Combine the numerators over the common denominator.

$\frac{x^{\frac{3}{2}}}{x^{\frac{3}{4}} y^{\frac{1 + 3}{4}}}$

Add $1$ and $3$ .

$\frac{x^{\frac{3}{2}}}{x^{\frac{3}{4}} y^{\frac{4}{4}}}$

Divide $4$ by $4$ .

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

Simplify $x^{\frac{3}{4}} y^{1}$ .

$\frac{x^{\frac{3}{2}}}{x^{\frac{3}{4}} y}$

Step 3

Move $x^{\frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 4

Multiply $x^{\frac{3}{2}}$ by $x^{- \frac{3}{4}}$ by adding the exponents.

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

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

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

$\frac{x^{\frac{3}{2} \cdot \frac{2}{2} - \frac{3}{4}}}{y}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{x^{\frac{3 \cdot 2}{2 \cdot 2} - \frac{3}{4}}}{y}$

Multiply $2$ by $2$ .

$\frac{x^{\frac{3 \cdot 2}{4} - \frac{3}{4}}}{y}$

Combine the numerators over the common denominator.

$\frac{x^{\frac{3 \cdot 2 - 3}{4}}}{y}$

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{x^{\frac{6 - 3}{4}}}{y}$

Subtract $3$ from $6$ .

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