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Exponents

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by vanesslondon » Tue Sep 23, 2008 4:32 am
Hello,
I'm finding exponents so hard - could someone pls explain the following to me?

How does (1.701)^-13
___________
(3.402)^-7


become the following when simplified:

(3.402)^7
__________
(1.701)^13

I just don't get it - any advice as well as where to learn more abuot this gratefully received. It is part of a MGMAT CAT question, but I don't think the MGMAT chapter on exponents helps with this.

Many thanks!
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by Morgoth » Tue Sep 23, 2008 4:43 am
Here is a basic rule for exponents

2^2 * 2^3 = 2^(2+3) = 2^5

2^5 / 2^3 = 2^(5-3) = 2^2

2^-2 = 1 / 2^2


Similarly,

(1.701)^-13
__________
(3.402)^-7

(1.701)^-13 = 1/(1.701)^13

(3.402)^-7 = 1/(3.402)^7

1/(1.701)^13 divided by 1/(3.402)^7 = (3.402)^7 / (1.701)^13

Just like 1/x / 1/y = y/x

Let me know if you have any doubts.
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by jsl » Tue Sep 23, 2008 4:44 am
Hiya!

Best to take a simpler example for this "property" of exponents. Basically, where you have exponents and a numerator/denominator, you can just flip it's location.

E.g....

3^-1 = 1 x (3^-1) = 1/3

1/(3^-1) = 3/1 = 3

Another example may be...

2^-2 = 1 x (2^-2) = 1/(2^2) = 1/4

I'm sure there's a good web link out there explaining this stuff - may be someone knows one?
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by mals24 » Tue Sep 23, 2008 4:45 am
Just remember this

(a)^-n can be written as (1/(a)^n)
For instance 4^-2 can be written as (1/(4)^2)

[1/(a)^-n] can be written as a^n
For instance [1/(4)^-2] can be written as 4^2


so (1.701)^-13 can be written as [1/(1.707)^13]
And [1/(3.402)^-3] can be written as (3.402)^3

So the fraction now changes to [(3.402)^3]/[1/(1.707)^13]

Hope you get the logic
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by vanesslondon » Tue Sep 23, 2008 4:48 am
You guys are absolutely amazing - thank you thank you thank you! I had learnt the rule and could 'see' it here - thanks so much for the detailed and quick responses!
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