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Rational Exponents with Negative Coefficients - Problem 2

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!

Solving an expression with a negative and a rational exponent. So for this problem what we need to figure out is, is the negative associated with the power and if it is what that means.

Looking at this, the negative is inside the parenthesis which tells us that it is actually associated with this exponent, so now we need to figure out what this exponent means. Power over root us that our power is 5 and our root is 3, so really what this tells is I'm looking at -27 to the 1/3 to the 1/5.

So we have the cube root, remember 1 over 3 is the same thing as cube root of -27. We can take the odd power of a negative number, so -27 to the 1/3 is actually just -3 and then we're taking that to be 1/5, -3 to the 1/5 , 3, 9, 27, 81 and I believe it's 243 after that, so we have 5 and it is negative so this is going to be -243.

So using our rules of fractional exponents and making sure we have the negative in the right spot, you will be able to solve this problem.

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