![]() \(\displaystyle\frac\) using only positive exponents and simplify. It's correct either way.Version 1: Use the negative exponent rule and then quotient ruleįirst, we apply the negative quotient rule that says as long as all the factors are being multiplied or divided together (no addition or subtraction) then we can move a factor with a negative exponent to the opposite side of a fraction and change the exponent to a positive. Rational exponents are fractional exponents (rational ratio), where both the numerator and denominator of the fraction are non-zero integers. 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. For example, when you see x-3, it actually stands for 1/x3. 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. Next, since we need positive exponents, we can use the quotient rule for the x's and y's separately. A negative exponent helps to show that a base is on the denominator side of the fraction line. 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. If you distribute the -11 to both of the equations, like so: (94)-11 (75)-11. 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 If you are given a factor with a negative exponent in the denominator. First, we're going to take care of what's in the parentheses by adding exponents. Factors in the numerator with a negative exponents move to the denominator. 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. ![]() Raised the entire denominator to the numerator because of the negative exponent. Write the expression with positive exponents. ![]() You might want to think of it this way: Multiplying out the numerator and denominator gives us. Vocabulary : A base with a negative exponent must be changed to its reciprocal to make the exponent positive. Its the line between the numerator and denominator. No, thats not a bar where the fractions all hang out and have a good time. A negative exponent is usually written as a base number multiplied to the power of a negative number. Anyway If you dont know already, the main idea here is that exponents switch signs whenever theyre moved to the opposite side of a fraction bar. 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. 1.Get to know the basics of negative exponent expression. Could life be any more awesome right now? Note that a number to a negative exponent is not necessarily a negative number. 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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