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? Our first step is just to flip the numerator and denominator to get rid of all the negatives in the exponents. 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. A General Note: The Negative Rule of Exponents For any nonzero real number a a and natural number n n, the negative rule of exponents states that an 1 an a n 1 a n Example: Using the Negative Exponent Rule Write each of the following quotients with a single base. 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. A negative exponent helps to show that a base is on the denominator side of the fraction line.
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