Simplify 5^(-5/2)*5^(9/2)

$5^{- \frac{5}{2}} \cdot 5^{\frac{9}{2}}$

Multiply $5^{- \frac{5}{2}}$ by $5^{\frac{9}{2}}$ by adding the exponents.

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

$5^{- \frac{5}{2} + \frac{9}{2}}$

Combine the numerators over the common denominator.

$5^{\frac{- 5 + 9}{2}}$

Add $- 5$ and $9$ .

$5^{\frac{4}{2}}$

Divide $4$ by $2$ .

$5^{2}$

Raise $5$ to the power of $2$ .

$25$