Evaluate (9^(3/4))/(9^(1/4))

$\frac{9^{\frac{3}{4}}}{9^{\frac{1}{4}}}$

Step 1

Move $9^{\frac{1}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$9^{\frac{3}{4}} \cdot 9^{- \frac{1}{4}}$

Step 2

Multiply $9^{\frac{3}{4}}$ by $9^{- \frac{1}{4}}$ by adding the exponents.

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

$9^{\frac{3}{4} - \frac{1}{4}}$

Combine the numerators over the common denominator.

$9^{\frac{3 - 1}{4}}$

Subtract $1$ from $3$ .

$9^{\frac{2}{4}}$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$9^{\frac{2 (1)}{4}}$

Cancel the common factors.

Factor $2$ out of $4$ .

$9^{\frac{2 \cdot 1}{2 \cdot 2}}$

Cancel the common factor.

$9^{\frac{2 \cdot 1}{2 \cdot 2}}$

Rewrite the expression.

$9^{\frac{1}{2}}$

Step 3

Simplify the expression.

Rewrite $9$ as $3^{2}$ .

${(3^{2})}^{\frac{1}{2}}$

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

$3^{2 (\frac{1}{2})}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$3^{2 (\frac{1}{2})}$

Rewrite the expression.

$3^{1}$

Step 5

Evaluate the exponent.

$3$