AS Mathematics - Core 1 - Indices Problems

[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.

Homework Statement

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

Homework Equations

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.

 

[Mark44]

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

Homework Equations

The Attempt at a Solution

1) 25^1/2 = $\sqrt{25}$ = 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.

 

[Mark44]

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.

 

[novamatt]

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]

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.