SOLUTION: I need help with this radical equation and evaluating: 25^(-3/4)

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Question 255033: I need help with this radical equation and evaluating: 25^(-3/4)
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, it is not an equation. An equation equates something with an equal sign.
It is an expression .
What does

25%5E%28-3%2F4%29
mean
The minus sign says to take a reciprocal
so it is really 1%2F25%5E%283%2F4%29
the 3 of 3/4 says to cube it
1%2F%2825%2A25%2A25%29%5E%281%2F4%29
=
1%2F%28%285%2A5%29%2A%285%2A5%29%2A%285%2A5%29%29%5E%281%2F4%29


1%2F%285%5E%284%2F4%29%2A5%5E%282%2F4%29%29

the 4 says to take its fourth root. 1%2F5sqrt%285%29

but we try not to leave radicals in the denominator.
So we multiply by sqrt%285%29%2Fsqrt%285%29
which yields
sqrt%285%29%2F25