Simplify (3^4d^(-3/4))/(3^2d^(3/4))

$\frac{3^{4} d^{- \frac{3}{4}}}{3^{2} d^{\frac{3}{4}}}$

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

$\frac{3^{4}}{3^{2} d^{\frac{3}{4}} d^{\frac{3}{4}}}$

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

Move $d^{\frac{3}{4}}$ .

$\frac{3^{4}}{3^{2} (d^{\frac{3}{4}} d^{\frac{3}{4}})}$

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

$\frac{3^{4}}{3^{2} d^{\frac{3}{4} + \frac{3}{4}}}$

Combine the numerators over the common denominator.

$\frac{3^{4}}{3^{2} d^{\frac{3 + 3}{4}}}$

Add $3$ and $3$ .

$\frac{3^{4}}{3^{2} d^{\frac{6}{4}}}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$\frac{3^{4}}{3^{2} d^{\frac{2 (3)}{4}}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{3^{4}}{3^{2} d^{\frac{2 \cdot 3}{2 \cdot 2}}}$

Cancel the common factor.

$\frac{3^{4}}{3^{2} d^{\frac{2 \cdot 3}{2 \cdot 2}}}$

Rewrite the expression.

$\frac{3^{4}}{3^{2} d^{\frac{3}{2}}}$

Factor $3^{2}$ out of $3^{4}$ .

$\frac{3^{2} \cdot 3^{2}}{3^{2} d^{\frac{3}{2}}}$

Cancel the common factors.

Factor $3^{2}$ out of $3^{2} d^{\frac{3}{2}}$ .

$\frac{3^{2} \cdot 3^{2}}{3^{2} (d^{\frac{3}{2}})}$

Cancel the common factor.

$\frac{3^{2} \cdot 3^{2}}{3^{2} d^{\frac{3}{2}}}$

Rewrite the expression.

$\frac{3^{2}}{d^{\frac{3}{2}}}$

Raise $3$ to the power of $2$ .

$\frac{9}{d^{\frac{3}{2}}}$