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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.

After watching this video lesson, you will be able to evaluate any exponents with decimal bases. Learn what the exponent does to the decimal and how to get your answer.

In this video lesson, we talk about exponents with decimal bases. **Exponents** are the specified powers that a number is raised to. **Decimals** are numbers with a decimal point. An exponent with a decimal base will have a decimal raised to a certain power.

Who uses these numbers? Scientists do and, of course, mathematicians. They are used to show the growth of certain things like the population growth of bacteria. You will see your numbers written out like 2.1^3 and 5.43^4.

These exponents with decimal bases can actually be evaluated. You can actually arrive at one number that is your answer. How do you evaluate these numbers, then? The exponent is the key. The exponent tells you how many times to multiply your decimal by itself. If the exponent is 3, then you multiply the decimal by itself 3 times. So 2.1^3 = 2.1 * 2.1 * 2.1. Then, to get your answer, you go ahead with the multiplication. 2.1 * 2.1 = 4.41. Multiplying the 4.41 with the 2.1 again, we get 4.41 * 2.1 = 9.261. So our answer is 9.261.

Alternately, you could use your calculator's ability to compute a number to any power. The button usually shows *x*^*y*. You will need to look at your calculator's manual to figure out whether you need to punch in the decimal first before pushing the button or the power first. Usually, you punch in your decimal, then you push the *x*^*y* button, then the exponent. Then, you push 'equal' to get your answer.

Evaluating these problems is pretty straightforward. Look at the exponent to find out how many times to multiply your decimal together. Then, you go ahead and multiply your decimal that many times. If your decimal is 4, then you multiply your decimal 4 times together.

Let's look at a couple of examples.

*Evaluate 1.2^4.*

The exponent here is 4. So, we need to multiply our 2.1 four times. 1.2^4 = 1.2 * 1.2 * 1.2 * 1.2. Evaluating this, we get 1.2 * 1.2 * 1.2 * 1.2 = 1.44 * 1.2 * 1.2 = 1.728 * 1.2 = 2.0736. Using a calculator, you also get 2.0736.

Let's look at one more example:

*Evaluate 4.11^3.*

See if you can do this one on your own. What do you do first? You first look at your exponent. What is your exponent? It is 3. What does this tell you? It tells you that you need to multiply your decimal three times. You can write out your problem now as 4.11^3 = 4.11 * 4.11 * 4.11. Evaluating this, you get 4.11 * 4.11 * 4.11 = 16.8921 * 4.11 = 69.426531. Using a calculator, you also get the same answer.

Let's review what we've learned.

In this video lesson, we talked about exponents with decimal bases. **Exponents** are the specified powers that a number is raised to. **Decimals** are the numbers with a decimal point.

To evaluate an exponent with a decimal base, we look at the exponent. This tells us how many times to multiply the decimal by itself. We, then, go ahead with the multiplication. We can alternately use our calculator to help us find the answer.

When you are done, you should be able to evaluate an exponent with a decimal base both manually and with your calculator's exponent function.

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

- What Are the Five Main Exponent Properties? 5:26
- How to Define a Zero and Negative Exponent 3:13
- Exponents with Fractional Bases 5:00
- Exponents with Decimal Bases 4:15
- Rational Exponents 3:22
- Simplifying Expressions with Rational Exponents 7:41
- Multiplying With Exponents 6:39
- Scientific Notation: Definition and Examples 6:49
- How to Use Exponential Notation 2:44
- Simplifying and Solving Exponential Expressions 7:27
- Exponential Expressions & The Order of Operations 4:36
- Multiplying Exponential Expressions 4:07
- Dividing Exponential Expressions 4:43
- The Power of Zero: Simplifying Exponential Expressions 5:11
- Negative Exponents: Writing Powers of Fractions and Decimals 3:55
- Go to 6th-8th Grade Math: Exponents & Exponential Expressions

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