Well this one can be a little bit and big ambiguous and if people are strict about order of operations, you should really be thinking about the exponent before you multiply by this -1. And, if you given a go at that, think about whether this should mean something different then that. ![]() And I encourage you to actually pause the video and think about with this right over here would evaluate to. Now there's one other thing that I want to clarify – because sometimes there might be ambiguity if someone writes this. And a negative times a positive is a negative, which we already learned from multiplying negative numbers. And you just really have to remember that a negative times a negative is a positive. So there's really nothing new about taking powers of negative numbers. So this right over here is going to give you a positive value. Or when you take the product of the two negatives, you keep getting positives. So the negatives and the negatives all cancel out, I guess you could say. And so when you do it an even number of times, doing it a multiple-of-two number of times. And if you take a negative base, and you raise it to an even power, that's because if you multiply a negative times a negative, you're going to get a positive. But then you have one more negative number to multiply the result by – which makes it negative. And that's because when you multiply negative numbers an even number of times, a negative number times a negative number is a positive. Whenever we raised raised a negative base to an exponent, if we raise it to an odd exponent, we are going to get a negative value. But positive 9 × -3, well that's that's -27. 3 × -3, we already figured out is positive 9. So we're going to multiply them together. What is this going to be equal to? Well, we're going to take 3 -3's, – and we're going to multiply them together. Let's take -3 and raise it to the 3rd power. ![]() Let's see if there is some type of pattern here. What's that going to be? Well a negative times a negative is a positive. Now what happens if you were take a -3, and we were to raise it to the 2nd power? Well that's equivalent to taking 2 -3's, so a -3 and a -3, and then multiplying them together. And there's nothing left to multiply it with. Well that literally means just taking a -3. Let's first think about what it means to raise it to the 1st power. So let's first think about – Let's say we have -3. Let's see if we can apply what we know about negative numbers, and what we know about exponents to apply exponents to negative numbers.
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