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Rational Exponents with Negative Coefficients - 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!

Simplifying an expression with a negative and a rational exponent. So for this what we need to do is figure out first if the negative is associated with the power and second what that power is actually telling us.

So the negative is inside the parenthesis which means that it is actually associated with this power. Now I have to deal with what this exponent means power over root will tell us that we're dealing with the second power in a cube root.

So 125 to the 1/3 all squared. So the 1/3 is telling us the cube root, so we're trying to find the cube root of 125 which is 5. The negative can be involved in a cube root so we end up with -5 quantity squared. When we square a negative we actually end up with a positive, so this turns out to be 25.

So using our laws of exponents and making sure we follow this negative through, you're able to find your answer.

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