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1. These questions are confusing.
I basically don't know how to work out the answer...

x = 3m and y = 3n

Express in terms of x and y:
a) 3m+n
b) 32n

Thank you!
2. (Original post by RosaA)
These questions are confusing.
I basically don't know how to work out the answer...

x = 3m and y = 3n

Express in terms of x and y:
a) 3m+n
b) 32n

Thank you!
Okay, so you need to use this rules. . That is, if the 'bases' are the same and the powers different, when you multiply the two numbers, you add the powers.

Conversely, if you're adding the powers you can split into . In this case, you're working with - can you take it from here?

For the second part, you also need to make use of the fact that . So: for example. You can verify this yourself with a calculator.

In this case, we have .
3. (Original post by RosaA)
...
Here's a quick intuitive feel for . I'll do it with here to make life simpler, but it works for any :

and

So:

You now have a product of 's and 's and there are threes being multiplied in total.

Hence as expected.
4. (Original post by RosaA)
...
And here's a quick intuitive argument as to why is , it'll use the other theorem we 'proved' above.

You're comfortable that now, I hope.

So, since:

then we can simply add their powers:

Since (i.e: x added to itself y times) is just .
5. (Original post by Zacken)
Okay, so you need to use this rules. . That is, if the 'bases' are the same and the powers different, when you multiply the two numbers, you add the powers.

Conversely, if you're adding the powers you can split into . In this case, you're working with - can you take it from here?

For the second part, you also need to make use of the fact that . So: for example. You can verify this yourself with a calculator.

In this case, we have .
Yup, that makes more sense now.
I didn't realise that if the "bases" are the same you could simply just add the powers like normal. I just need 2 get remember that now and I'll be fine. Thank you!

In terms of the second question, I understand it now.
I've just realised how simple it was *laughs*

I didn't occur to me to use any of the index laws -which was the issue, so thank you for going over them for me
6. (Original post by RosaA)
Yup, that makes more sense now.
I didn't realise that if the "bases" are the same you could simply just add the powers like normal. I just need 2 get remember that now and I'll be fine. Thank you!

In terms of the second question, I understand it now.
I've just realised how simple it was *laughs*

I didn't occur to me to use any of the index laws -which was the issue, so thank you for going over them for me
Haha, no problem - I wrote all of that in seperate posts so I can link back to this thread when other people have the same questions instead of me having to type it up all over again, hope you didn't mind!

7. (Original post by Zacken)
Haha, no problem - I wrote all of that in seperate posts so I can link back to this thread when other people have the same questions instead of me having to type it up all over again, hope you didn't mind!

That's fine by me -
8. (Original post by RosaA)
That's fine by me -
Awesome.

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