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 -

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:

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

Hope this helps!

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In general:
x^a/b = b-root(x^a)

Thank you so kindly.

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- outRider -