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## equivalent values

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### #1outRider  Members

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Posted 05 October 2001 - 03:50 PM

I find myself having to find alternate representations of different types of terms, basically fractional and exponential representations, to solve certain problems. I can''t for the life of me remember what equals what. For example I know that 1 / x^4 = x^-4 and 3x^-4 = 3 / x^4 Here''s the ones I''m havin trouble with, I need the fractional/exponential representation for each. I know that I might actually list both representations. aX^n = aX^-n = a / bX^n = a / bX^-n = -a / bX^n = -a / bX^-n = X^1/2 = sqrt(X) ? X^-a/b = a / X^b/c = I know thats a lot, so if anyone has even just a few examples that would work in any case then that might be better. Thanks in advance to anyone who can help. ------------ - outRider -

### #2Dean Harding  Members

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Posted 05 October 2001 - 05:03 PM

All you need to remember is that a negative exponent means you invert the fraction. ie:

x-n = 1/xn

or

1/x-n = xn

Also, the denominator of an exponent is the same as the order of the root of the number, for example:

x1/2 = sqrt(x)
x1/3 = cuberoot(x)
x3/2 = sqrt(x3)
x-3/2 = sqrt(x-3) = sqrt(1/x3)

Hope this helps!

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### #3Scarab0  Members

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Posted 05 October 2001 - 08:57 PM

In general:
xa/b = b-root(xa)

### #4outRider  Members

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Posted 07 October 2001 - 10:36 AM

Thank you so kindly.

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- outRider -

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