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Evaluating Rational Exponents - Problem 1

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Simplifying a expression with a rational exponent. So whenever we're just simplifying this, what we need to remember is that exponent is really just saying the power and the root that we're concerned with. So what we have here is 25 to the 3 halves. The 3 is the power, the 2 is the root, power over root and what we need to do is just basically break it down into components, the power and the root.

I don't know what 25 to the third is so what that tells me is I need to do the root first, to make the numbers smaller and then what I do by that is basically take 25, the root is the denominator, the power is the numerator, so rewrite it as 25 to the 1 half to the third. If we distribute this through we would end up with the same thing.

So what I have here is 25 to the 1/2. 1/2 is just telling me I'm dealing with the square root, square root of 25 is 5 and we still have to the third. 5³ is just 125, so by remembering that we have power over root, we're able to rewrite our expression and then just do two fairly easy steps in order to simplify.

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