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Rational Exponents

Rational Exponents Math 113

Suppose X=7^(1/3). What would X^3=7^(1/3) be? X=7^1 or 7
If X^3 = 7. Then X = the cubed root of 7. This means that the cubed root of 7 is = to Cube root of 7 = 7^(1/3)
4^(3/2) = (Square root of 4) ^ 3. = (2)^3 = 8
25^(3/2) = (sqrt of 25)^ 3 = (5)^3 = 125
4^(-4/2) = 1/4^(4/2) = 1/ sqrt of 4 ^4 = 1/2^4 = 1/16
16^(-5/4) = 1/16(5/4) = 1/ fourth root of 16 ^ 5 = 1/2^5 = 1/32
A^(2/2) Multiplied by A^(8/2) = A^(8/2) = A^4
A^0 = 1. A cannot equal 0
A^(-n) = 1/A^(N) = A cannot equal 0
(The fourth root of x)^2 = X^(2/4)= X^(1/2)= Sqrt of X.
The 6th root of 25 = 25^(1/6) = (5^2)^1/6 = (5)^2/6 = (5)^1/3 = Cubed root of 5.
Created by: Skymarie