Simplify (3^(11/5))÷(3^(-9/5))

$3^{\frac{11}{5}} \div 3^{- \frac{9}{5}}$

Step 1

Rewrite the division as a fraction.

$\frac{3^{\frac{11}{5}}}{3^{- \frac{9}{5}}}$

Step 2

Move $3^{- \frac{9}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3^{\frac{11}{5}} \cdot 3^{\frac{9}{5}}$

Step 3

Multiply $3^{\frac{11}{5}}$ by $3^{\frac{9}{5}}$ by adding the exponents.

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

$3^{\frac{11}{5} + \frac{9}{5}}$

Combine the numerators over the common denominator.

$3^{\frac{11 + 9}{5}}$

Add $11$ and $9$ .

$3^{\frac{20}{5}}$

Divide $20$ by $5$ .

$3^{4}$

Step 4

Raise $3$ to the power of $4$ .

$81$