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Rational Exponents - Problem 3

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!

Rewriting a expression with rational exponents as an expression with the square roots. So the main part about this exercise that we're going to be focusing on, is the association of powers, making sure we associate the power with the right thing and also translating these exponential fractions into the right roots.

So starting with this first term. The first thing we need to realize is that this 4/5 is not associated with this 4. So the 4 just stays in the front and then we're left with x to the 4/5. Fractional exponents are power over root, so this is then x to the 4th with the 5th root out in front. And this 4 could be either inside or outside of the radical, it doesn't really matter. Order of operations will take care of it. Plus 3y to the 2/3. In this case the 2/3, the exponent is associated with both the 3 and the y. Over here, with your exponents before you multiply so this exponent is only with the x.

So we have 3y and then to the 2/3 power over root, so this is going to be the cube root and this one let's have the power on the outside. Again it doesn't matter which, these are going to be the same exact thing if you multiply them, out.

So just by looking at it, you will bring power over root and to check for your exponential associations, you will be able to take this expression using rational exponents and rewrite it using radicals.

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