Evaluate each expression 125^(-1/3)

Question

Accepted Answer

Welcome back, I'm so glad you're here, we are simplifying the expression 343 raised to the negative one third. And when we see that negative in the exponent, we want to think oh my goodness, we need to flip that around. So because that 343 is just a regular number in the numerator, we're going to put it down in the denominator. If it were in the denominator we flip it up to the numerator and now you That negative sign is gone from the exponent. So we're dealing with one over 343 to the one third and great, but we still have to deal with that one third. So we've got a fraction for an exponents. We're going to look at the one on the bottom way down in the roots and the like the roots of a tree and that's going to go inside the root here when we rewrite it. And this number up here in the exponent floating web in the sky that is going to remain our exponent, that's in the numerator. The one. So we can rewrite this, we keep our one over, bring that down and we've got the 343 but we're going to take the cubed root of 343 and it's going to be raised to the exponent one. Well we don't really have to worry about that because it's just going to be itself once we do that but we can simplify, we know the cubed root of 343 is seven and seven race to the one is seven, so that's as simplified as it's going to get. We look at our answer choices and 1/7 is answer choice A. That's it. You've done it. Well done. We'll catch you on the next one.