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## Reciprocal?

This topic has 1 expert reply and 0 member replies
klaud Just gettin' started!
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Reciprocal? Thu Mar 15, 2012 10:42 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
How can i solve this?

(1/4)^-1/4

(4)^-1/2

(1/4)^1/4

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### GMAT/MBA Expert

Mike@Magoosh GMAT Instructor
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Thu Mar 15, 2012 4:21 pm
Hi, there. I'm happy to help with these.

First of all. Negative exponents. A negative exponent means take the reciprocal.

a^(-n) = 1/(a^n)

(1/b)^(-n) = b^n

(a/b)^(-n) = (b/a)^n

Now, fractional exponents. A fraction exponent indicates a root.

a^(1/2) = sqrt(a)

a^(1/3) = cube root of a

a^(1/4) = fourth root of a

a^(3/5) = fifth root of (a^3) = [fifth root of a]^3

Other exponent rules:

(a^m)*(a^n) = a^(m + n)
(a^m)/(a^n) = a^(m - n)
[a^m]^n = a^(m*n)

1) (1/4)^-1/4 = 4^(1/4) = [4^(1/2)]^(1/2) = 2^(1/2) = sqrt(2)

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

3) (1/4)^1/4 = [(1/4)^(1/2)]^(1/2) = (1/2)^(1/2) = 1/sqrt(2)

Does this make sense? Here's a free lesson video on exponents:

http://gmat.magoosh.com/lessons/216-intro-to-exponents

Just so you know, at Magoosh we have 200+ lesson videos and 800+ practice questions, each with its own video explanation --- all for a fraction of the price of other test prep sources. If you have lots of questions on basic math, Magoosh video lessons might be the key for you.

Let me know if you have any questions.

Mike

_________________
Magoosh GMAT Instructor
http://gmat.magoosh.com/

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