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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

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:

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.

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.

If we wanted to evaluate this problem, we can go ahead with the multiplication problem, or we can use our calculator to help us calculate our negative number raised to a certain power. Because our base is a negative number, our answers could be either positive or negative. If we have an odd exponent, then our answer will be negative. If we have an even exponent, then our answer will be positive.

For example:

- (-2)^3 = -2 * -2 * -2 = -8. The answer is negative because our exponent is odd.
- -(3)^4 = -3 * -3 * -3 * -3 = 81. Our answer here is positive because our exponent is even.

Let's look at an example. Rewrite -8 * -8 * -8 using an exponent, and then evaluate it.

Here we are asked to rewrite -8 * -8 * -8 with exponents. We ask ourselves, how many times are we multiplying the -8? We are multiplying the -8 three times, so our exponent is 3. We can rewrite -8 * -8 * -8 as (-8)^3. Evaluating this, we get -512. Our answer is negative because our exponent is odd.

Let's review what we've learned. **Exponents** are the powers that numbers are raised to. **Bases** are the numbers that are being raised to a certain power. If we have a string of the same negative number being multiplied together, we can rewrite it with exponents. The exponent tells us how many times our negative number is being multiplied. We can evaluate these exponents by either multiplying it or using our calculator to help us evaluate a given number to a certain power.

Once you are finished, you should be able to:

- Recall how to solve a math problem with exponents
- Rewrite a math problem using exponents and solve

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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