## AS Mathematics - Core 1 - Indices Problems

I am struggling with my mathematics indices homework. I think I have some correct answers so far but I'm pretty stumpted on some others. How would I go about solving the following equations.

1. The problem statement, all variables and given/known data
1) 25 to the $\frac{1}{2}$ - $\frac{5 to the -4}{5 to the -5}$

2. Relevant equations

3. The attempt at a solution
1) 25 to the $\frac{1}{2}$ = $\sqrt{25}$ = 5 i know that
i get lost on the next bit... i end up with
$\frac{-625}{-3215}$ and therefor
5 - $\frac{1}{5}$ = 4$\frac{4}5{}$ but this is not in index form?? if i take it further...
$\sqrt[5]{4}$ to the 4 and from there i have no idea how to go further, plus i am positive i've gone wrong at a much earlier stage.
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Mentor
 Quote by novamatt I am struggling with my mathematics indices homework. I think I have some correct answers so far but I'm pretty stumpted on some others. How would I go about solving the following equations.
 Quote by novamatt 1. The problem statement, all variables and given/known data 1) $$25^{1/2}- \frac{5^{-4}}{5^{-5}}$$ 2. Relevant equations 3. The attempt at a solution 1) 251/2 = $\sqrt{25}$ = 5 i know that i get lost on the next bit... i end up with $\frac{-625}{-3215}$ and therefor 5 - $\frac{1}{5}$ = 4$\frac{4}5{}$ but this is not in index form?? if i take it further... $\sqrt[5]{4}$ to the 4 and from there i have no idea how to go further, plus i am positive i've gone wrong at a much earlier stage.
 Mentor Use the fact that a-n = 1/an. Also, at this stage in mathematics, we pretty much never write things like 4 $\frac{4}{5}$. It looks too much like 4 * 4/5. Instead of mixed numbers like this, improper fractions such as 24/5 are preferred.