Given:
Consider the given expression is
[tex]5^{-\frac{5}{2}}\times 5^{\frac{9}{2}}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]5^{-\frac{5}{2}}\times 5^{\frac{9}{2}}[/tex]
Using properties of exponents, we get
[tex]=5^{-\frac{5}{2}+\frac{9}{2}}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]=5^{\frac{-5+9}{2}}[/tex]
[tex]=5^{\frac{4}{2}}[/tex]
[tex]=5^{2}[/tex]
[tex]=25[/tex]
Therefore, the simplified form of given expression is 25.
