![]() Here's a good place to take a look at comparing negative and positive exponents and seeing how they behave on a graph. Then solve as usual with the power rule.ĭefinitely not as confusing as it first looked, right? Numerators and denominators are the key ingredients that make fractions. Our first step is just to flip the numerator and denominator to get rid of all the negatives in the exponents. Knowing how to get rid of negative exponents is key to fully simplifying an. With that in mind, let's work through the question. If you move it to the numerator, its exponent also becomes positive. The same actually works for negative exponents on the bottom. If you ever see a negative exponent on the top of a fraction, you know that if you flip it to the bottom, it'll become positive. ![]() So moving on from the above, we can continue solving with the negative exponent as we did before.Īs you can see, the final answer we get is negative!. However, keeping the -1 outside helps us work with the negative exponent a little easier and allows us to illustrate what's happening. Multiplying in that -1 will turn the equation back into what it was originally. One way you can rewrite the question we're given is the following: Again, just move the number to the denominator of a fraction to make the exponent positive. 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. This would give us 1/3.A negative exponent helps to show that a base is on the denominator side of the fraction line. If we wanted to simplify 3 -2 we would take the reciprocal of 3. Another way to think about this is by stating that we will drag the base and exponent across the fraction bar and make the exponent positive. When we want to simplify with negative exponents, we take the reciprocal of the base and make the exponent positive. This was just to give you an understanding of where our simplified result comes from. Obviously, we will not be going through all this division each time we need to simplify with negative exponents. Divide by the base (3) each time we reduce the exponent by 1: 1 would be divided by 3, and could be written as 1/3:Īs we continue to decrease our exponent by 1, we continue the same process. ![]() What happens if we continue and decrease the exponent by 1 to (-1)? We would continue the pattern. Therefore, we say zero raised to the power of zero is undefined. We can't divide 0 by 0, this is undefined. If we try to raise zero to the power of zero, we will have a problem. We can state that any non-zero number raised to the power of zero is 1. So what happens when we get to 3 0? We continue the same pattern. If we want 3 1, we can divide 9 by 3 to obtain 3. If we move to 3 2, we can divide 27 by 3 to obtain 9. When we go from 3 4 (81) to 3 3 (27), we could just divide 81 by 3 to obtain 27. This is because we are removing a factor of 3 when we decrease the exponent by 1. ![]() What is the value of 3 to the power of (-4)? To understand negative exponents, let's think about a pattern:Įach time we reduce our exponent by 1, we divide by our base of 3. What happens if we see something such as: Negative Exponents & the Power of Zero Up to this point, we have only dealt with whole-number exponents larger than 1. In this lesson, we will expand on our knowledge of the rules of exponents and learn about negative exponents, the power of zero, and the quotient rule for exponents. ![]()
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