Exponents

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vanesslondon: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon May 21, 2007 12:00 am

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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Source: Beat The GMAT — Problem Solving | Tue Sep 23, 2008 4:32 am

Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

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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jsl: Master | Next Rank: 500 Posts; Posts: 203; Joined: Wed Jun 04, 2008 1:01 am; Location: Windsor; Thanked: 5 times; GMAT Score:650

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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mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

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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vanesslondon: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon May 21, 2007 12:00 am

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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