multiplying by 1/3
... (1/x) / [x^(-2/3)] = 1 / [x^(1/3)]
multiplying by x^(-2/3)
... 1/x = [x^(-2/3)] / [x^(1/3)]
... = 1 / [x^(3/3)] = 1/x
Hi, I have a question regarding simplifying the following expression:
(1/x)/((1/3)x^(-2/3)) = 3/3sqrtx
The last expression reads three over cube root of x. I don't understand how to get from the expression on the left side of the equal sign to the one on the right.
Could somebody please help me out?
Your help would be greatly appreciated!
3 answers
re-writing your equation:
(1/x)/((1/3)x^(-2/3)) = 3/x^(1/3)
(3/x) x^(2/3) = 3/ x^(1/3)
divide by 3
(1/x) x^(2/3) = 1/x^(1/3)
multiply both sides by x^(1/3)
(1/x)(x)^1 = 1
1 = 1
so the equation is true for all x, except of course x = 0, or else we would be dividing by zero
(1/x)/((1/3)x^(-2/3)) = 3/x^(1/3)
(3/x) x^(2/3) = 3/ x^(1/3)
divide by 3
(1/x) x^(2/3) = 1/x^(1/3)
multiply both sides by x^(1/3)
(1/x)(x)^1 = 1
1 = 1
so the equation is true for all x, except of course x = 0, or else we would be dividing by zero
Thank you for your help, Scott and Reiny.
1 answer