Exponents with Decimal Bases

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  • 0:01 Exponents With Decimal Bases
  • 2:08 Examples
  • 3:42 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.

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.

Exponents with Decimal Bases

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.

How to Evaluate

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.

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