# 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.

## Homework Statement

1) 25 to the $\frac{1}{2}$ - $\frac{5 to the -4}{5 to the -5}$

## 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.

## Answers and Replies

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Mark44
Mentor
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.
Edited to make readable.

## Homework Statement

1) $$25^{1/2}- \frac{5^{-4}}{5^{-5}}$$

## 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.

Mark44
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.

thanks for the assistance its a bit late for me to crack on with the problem at the moment I will return tomorrow and have another go.

Could you please tell me how you put the 1/2 index power or direct me to a link where I can learn how to do this... is it simply html code like the ones provided on your symbol toolbar?

Mark44
Mentor
You can write exponents, as we in the US call them, by clicking Go Advanced, which opens another menu. Use the X2 button to make exponents.