Simplify ((-3x^(3/2))^3*y^(3/2))/(y^3)

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

Move $y^{\frac{3}{2}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

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

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

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

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

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

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

Combine $3$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{{(- 3 x^{\frac{3}{2}})}^{3}}{y^{\frac{6 - 3}{2}}}$

Subtract $3$ from $6$ .

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

Simplify the numerator.

Apply the product rule to $- 3 x^{\frac{3}{2}}$ .

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

Raise $- 3$ to the power of $3$ .

$\frac{- 27 {(x^{\frac{3}{2}})}^{3}}{y^{\frac{3}{2}}}$

Multiply the exponents in ${(x^{\frac{3}{2}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 27 x^{\frac{3}{2} \cdot 3}}{y^{\frac{3}{2}}}$

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

Combine $\frac{3}{2}$ and $3$ .

$\frac{- 27 x^{\frac{3 \cdot 3}{2}}}{y^{\frac{3}{2}}}$

Multiply $3$ by $3$ .

$\frac{- 27 x^{\frac{9}{2}}}{y^{\frac{3}{2}}}$

Move the negative in front of the fraction.

$- \frac{27 x^{\frac{9}{2}}}{y^{\frac{3}{2}}}$