Once I've flipped the fraction and converted the negative outer power to a positive, I'll move this power inside the parentheses, using the power-on-a-power rule; namely, I'll multiply. In this case, this will result in negative powers on each of the numerator and the denominator, so I'll flip again. Yes, I'm kind of taking the long way 'round. Instead of flipping twice, I noted that all the powers were negative, and moved the outer power onto the inner ones; since "minus times minus is plus", I ended up with all positive powers.
Note: While this second solution would be a faster way of getting the exercise done, "faster" doesn't mean "more right". Either way is fine. Since exponents indicate multiplication, and since order doesn't matter in multiplication, there will often be more than one sequence of steps that will lead to a valid simplification of a given exercise of this type.
Don't worry if the steps in your homework look quite different from the steps in a classmate's homework. As long as your steps were correct, you should both end up with the same answer in the end. You can use the Mathway widget below to practice simplifying expressions with negative exponents.
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By the way, now that you know about negative exponents, you can understand the logic behind the "anything to the power zero" rule:. Why is this so? Fractions with negative exponents can be solved by taking the reciprocal of the fraction. Then, find the value of the number by taking the positive value of the given negative exponent. Learn Practice Download. Negative Exponents Negative exponents tell us that the power of a number is negative and it applies to the reciprocal of the number.
What are Negative Exponents? Negative Exponent Rules 3. Why are Negative Exponents Fractions? Multiplying Negative Exponents 5. How to Solve Negative Exponents? Have questions on basic mathematical concepts? Become a problem-solving champ using logic, not rules.
Learn the why behind math with our certified experts. Practice Questions on Negative Exponents. This happens because the reciprocal of a positive number is positive. As the image demonstrates, we are just multiplying a positive number by itself repeatedly. This video by mathman defines negative exponents and explains how to simplify them.
There are other exponent rules as well, including a product rule for exponents , a zero rule , and a power rule for exponents. Some rules we use in this explanation are useful for all types of exponents. This includes exponents that are negative numbers. Let's first look at an example that introduces negative exponents: x2x5. We can use the quotient rule to simplify this expression. Well, we can solve this problem a different way and find out.
They are two algebraic expressions that mean exactly the same thing. This leads us to our rule for negative exponents, which we can write in two different ways. Let's try another example. We will simplify x5x That is, if an answer has a negative exponent, rewrite the answer to use a positive exponent instead. That's why we have the last step in this example. Sometimes the expression we start with will have a negative exponent. However, that doesn't make things more difficult. Here's a good place to take a look at comparing negative and positive exponents and seeing how they behave on a graph.
Back to Course Index. You can still navigate around the site and check out our free content, but some functionality, such as sign up, will not work. If you do have javascript enabled there may have been a loading error; try refreshing your browser. Home Algebra Exponents. Still Confused? Nope, got it. Play next lesson. Try reviewing these fundamentals first Negative exponent rule. That's the last lesson Go to next topic.
Still don't get it? Review these basic concepts… Negative exponent rule Nope, I got it. Play next lesson or Practice this topic. Play next lesson Practice this topic. Start now and get better math marks! Intro Lesson. Lesson: 1.
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