![]() In this case, we've got a negative number with a negative exponent. Then, solving for exponents is easy once we have it in a more calculation-friendly form. We'll start with regular numbers with a negative exponent, then move on to fractions that have negative exponents on both its numerator and denominator.Īs we learned earlier, if we move the number to the denominator, it'll get rid of the negative in the exponent. Let's try working with some negative exponent questions to see how we'll move numbers to the top or bottom of a fraction line in order to make the negative exponents positive. You'll soon understand all the basic properties of exponents! How to solve for for negative exponents There'll be a link to a chart at the end of this lesson that can show you how that relationship comes about. Learning this lesson will also help you get one step closer to understanding why any number with a 0 in its exponent equals to 1. That's the main reason why we can move the exponents around and solve the questions that are to follow. However, you can actually convert any expression into a fraction by putting 1 over the number. You might be wondering about the fraction line, since there isn't one when we just look at x^-3. For example, when you see x^-3, it actually stands for 1/x^3. In other words, the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice versa. It's correct either way.A negative exponent helps to show that a base is on the denominator side of the fraction line. When you get really good, you'll see that a -1 exponent really just flips the fraction. Of course, we're still inside the parentheses.įinally, the -1 exponent can be multiplied to both of the other exponents as well as the whole number in the numerator. Next, since we need positive exponents, we can use the quotient rule for the x's and y's separately. We can also take care of those pesky coefficients by dividing 10 by 5. We'll work inside out using the product and power rules. To start, we'll take care of the stuff inside the parentheses in both the numerator and denominator. We're sure it's no problem for a well-trained Shmooper like you.Īll we need to do is keep the x's with the x's and the y's with the y's, and deal with the coefficients separately. This is crazy-looking, but it's definitely a good summary of all our rules up to this point. Anyway, here's our work for this problem-o. But remember, anything raised to the 0 is 1. If you went ahead and did all the work for this one before realizing it was all raised to the power of 0, we apologize. ![]() In this particular problem, we multiply the -8 and 7 while adding the exponents. This tends to make things just a bit more confusing because we still need to treat the coefficients like normal numbers while applying exponent rules to the exponents. In this problem, the -8 and 7 are coefficients. In case you weren't awake in the first section, coefficients are the numbers in front of or multiplied by the variables. Simplify using positive exponents: (-8 z -6)(7 z 3). Next, we'll multiply 12 by 3 to get 36 before subtracting 4.Īs long as we can add, multiply, and subtract, we're golden.Īnyone ready for the coefficients? Sample Problem First, we're going to take care of what's in the parentheses by adding exponents. Yikes, we're going right for the jugular here all three rules at once. We need to take the lovely exponent in the numerator and subtract it from the exponent in the denominator. This is important in case we get asked to simplify using only positive exponents. The same thing works in the other direction too-if the bigger exponent is in the denominator. This leaves us with three x's, otherwise known as x 3. Since x divided by x is 1, we can divide out two x's on the top and bottom. That's five x's on top and just two x's below. ![]() You might want to think of it this way: Multiplying out the numerator and denominator gives us. This brings us to a new rule: whenever like bases are divided, we subtract the exponent in the denominator from the one in the numerator. Could life be any more awesome right now? Whenever a base is moved to the other side of a fraction bar, the exponent of that base switches from negative to positive. It's the line between the numerator and denominator. No, that's not a bar where the fractions all hang out and have a good time. If you don't know already, the main idea here is that exponents switch signs whenever they're moved to the opposite side of a fraction bar. That's simply because negative exponents have a bit of a mind of their own. You may or may not have noticed that you've yet to see any negative exponents. ![]()
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