Exponents with Negative Bases

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  • 0:05 Exponents with Negative Bases
  • 0:55 Using Exponents to Multiply
  • 1:54 How to Evaluate
  • 2:49 Example
  • 3:30 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can use exponents to help you multiply a string of negative numbers. Learn what kinds of negative numbers you can do this with and to write it.

Exponents with Negative Bases

In this video lesson, we will talk about exponents with negative bases. Exponents are the powers that numbers are raised to. Bases are the numbers that are being raised to a certain power. Exponents are written as a smaller number in the upper right corner to a number. If our base is negative, then we write our negative number inside a pair of parentheses like this:

exponent negative base

The -2 is our negative base and the 3 is our exponent. Who uses numbers like these? Scientists use these numbers to help them analyze situations. You will come across these numbers in your math classes and in your math tests. It will serve you well to know and understand how to work with these types of problems. In this video lesson, you will learn just that.

Using Exponents to Multiply

The exponent that you see tells you how many times to multiply your base. In our example with a base of -2 and an exponent of 3, the exponent of 3 is telling us to multiply the -2 by itself three times. We can actually rewrite our problem using just multiplication. We would get (-2)^3 = -2 * -2 * -2. Seeing how this works, we can use it to our advantage and rewrite a multiplication problem where we are multiplying the same negative number multiple times. For example, if we have -3 * -3 * -3 * -3, we can rewrite it as (-3)^4 because we are multiplying the -3 four times. The exponent of 4 tells us to multiply the -3 four times.

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