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.