![]() ![]() Especially if you look at order of operations, and you do your exponent first, this would be interpreted as -4 times 4, which would be -16. This one clearly evaluates to 16 – positive 16. What if someone had these to express its -4 or a -4 squared or -4 squared. So what if someone had give myself some more space here. You might say well what's what's the big deal here? Well what if this was what if these were even exponents. So many times, this will usually be interpreted as negative 2 to the third power, which is equal to -8, while this is going to be interpreted as -2 to the third power. You could this is implicitly saying -1 × 2^3. 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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