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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 evaluate fractions that have exponents attached to them. Learn how the numerator and denominator behave with exponents.

In this video lesson, we talk about fractions with exponents. **Fractions** are the numbers made up of an integer divided by another integer. **Exponents** are the number that a certain number is raised to. (1/2)^3, (3/4)^10, and (2/9)^4 are all examples of fractions with exponents. In math, we can also say that these are exponents with fractional bases. The base is the number that is being raised to our power.

For the fraction with an exponent (1/2)^3, the 1/2 is the base and the 3 is the exponent. Believe it or not, these problems are used in the real world to calculate things that happen in the real world. Scientists use these problems to calculate the decay of certain items. For example, we can say that light decays as you get further away from the light source. The further you go away from the light, the darker it gets. This decay of the light can be calculated mathematically with an exponent with a fractional base.

So, now that we know how these problems are used in the real world, let's see how scientists evaluate them. The process is straightforward and easy. The only rule that you have to remember is that when you see a fraction raised to a power, this power is applied to both the numerator and denominator.

So, you can actually rewrite each problem so that the numerator is raised to the power and the denominator is raised to the power as well. And then you evaluate the numerator and denominator separately. Then you simplify as much as you can to get your answer.

For example, to evaluate (1/2)^3, you can rewrite this problem as (1^3) / (2^3). See how we applied the power to both the numerator and denominator? Evaluating the numerator and denominator separately, you get 1/8 for your answer. This is as simplified as you can get, so this is your final answer.

Let's look at a couple more examples.

*Evaluate (3/4)^10*

Looking at this problem, we see that our fractional base is 3/4 and our exponent is 10. So our fraction 3/4 is being raised to the power of 10. Rewriting this and applying the power to both the numerator and denominator, we get (3^10) / (4^10). Evaluating the numerator and denominator, we get 59,049/1,048,576. Can we simplify this? No, so this means that we have found our answer. (3/4)^10 evaluates to 59,049/1,048,576.

Let's look at another one.

*Evaluate (2/4)^4*

Try to do this on your own. What is our first step? We apply the power to both the numerator and denominator and rewrite the problem so that both the numerator and denominator have an exponent. We get (2^4) / (4^4).

Now we can go ahead and evaluate the numerator and denominator with the exponent. We get 16/256.

Now, what is next? Yes, we need to see if we can simplify this fraction. Are there any numbers that both the numerator and denominator can be divided equally by? Yes, there is. So we need to go ahead and simplify this further. Both the numerator and denominator can be divided equally by 16. Dividing the numerator by 16, we get 1. Dividing the denominator by 16, we get 16. So our final answer then is 1/16 and we are done!

Let's review what we've learned.

**Fractions** are the numbers made up of an integer divided by another integer. **Exponents** are the number that a certain number is raised to. When you have an exponent with a fractional base, you will have problems such as (1/2)^3, (3/4)^10, and (2/9)^4.

To evaluate these problems, you first rewrite the problem so that the power is being applied to both the numerator and the denominator. Then, you evaluate the numerator and the denominator separately. Then, you see if you can simplify your answer. If you can't simplify your answer, then you have found your final answer. If you can simplify it, then your answer is the most simplified form.

After you have finished this lesson, you should be able to solve a fraction math problem that includes an exponent.

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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
- How to Simplify Expressions with Exponents 4:52
- 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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