Simplify (3y^(3/4))/(2xy^(3/2))

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

Step 1

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

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

Step 2

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

Move $y^{- \frac{3}{4}}$ .

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

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{3}{2 x y^{\frac{- 3 + 6}{4}}}$

Add $- 3$ and $6$ .

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