Simplify (9^(3/2)*9^(1/2))/(9^-2)

$\frac{9^{\frac{3}{2}} \cdot 9^{\frac{1}{2}}}{9^{- 2}}$

Step 1

Multiply $9^{\frac{3}{2}}$ by $9^{\frac{1}{2}}$ by adding the exponents.

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

$\frac{9^{\frac{3}{2} + \frac{1}{2}}}{9^{- 2}}$

Combine the numerators over the common denominator.

$\frac{9^{\frac{3 + 1}{2}}}{9^{- 2}}$

Add $3$ and $1$ .

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

Divide $4$ by $2$ .

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

Step 2

Move $9^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

Multiply $9^{2}$ by $9^{2}$ by adding the exponents.

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

$9^{2 + 2}$

Add $2$ and $2$ .

$9^{4}$

Step 4

Raise $9$ to the power of $4$ .

$6561$