# Comparing Exponents Worksheets

When a number is being multiplied by itself, we can write it in a much more elegant way using an expression where the number being multiplied serves as the base and the number of times it is being multiplied as the exponent. If we were multiplying 5 by itself 3 times, we could write it as 5^{3}. 5 is written in the position of the base and 3 is written as the exponent. In this topic we will learn how to compare values that are written with this type of notation. If the two values share a common base, you simply compare the exponents. The larger the exponent the larger the value. If they do not share a common base, you must convert the values to standard form and then make your comparison from there. These worksheets and lessons will help students learn how to compare the end values of exponents.

### Aligned Standard: 6.EE.A.1

- Step-by-Step Lesson- Students will eventually be able to complete this problem in two steps.
- Guided Lesson - We introduce negative exponents and the power of 1.
- Guided Lesson Explanation - Some of the problems just take a glance to figure out. Other problems require a calculator.
- Practice Worksheet - This is your basic starter worksheet on this topic.
- Matching Worksheet - We choose this approach because it was a recent National Exam.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

The homework works through the progression of the skill.

- Homework 1 - Convert to standard form and compare the following exponents.
- Homework 2 - Determine which exponent is greater than or less than.
- Homework 3 - Symbols will get it done here for you. Remember that we are always pointing to the smaller value.

### Practice Worksheets

These are tack on skill builders that work in sync with the worksheet above.

- Practice 2 - The space can be found below all this.
- Practice 3 - Use these symbols: >, <, or =.

### Math Skill Quizzes

The difficulty progresses with each successive worksheet.

- Quiz 1 - Show all your work here.
- Quiz 2 - Remember what the value of a negative exponent is before you proceed.
- Quiz 3 - Some of those fractions are sizable.

### How to Compare the Value of Exponents

We all know all know that the calculated expression of 4 x 4 is equal to 16, but what if we wanted to multiply 4 by itself 5 times or 10 times? There is a much shorter way to write these using exponents. It can be written as 4^{5} or 4^{10}. Letâ€™s focus on 4^{5} to discuss the components of an exponent. In this example the number 4 serves as the base. The base is the number that we will multiplying a fixed series of times. 5 is the exponent that indicates the number of times it will be multiplied by itself. So, this expression indicates that we will multiply 4 by itself, 5 times. It can be written as 4 x 4 x 4 x 4 x 4, but as you can see exponents provide us with a much more elegant way to write it.

When we need to compare to values that are written with exponents you will come across two common types of comparisons. The first is a comparison between values that share a common base such as: 8^{6} and 8^{4}. In this case, both values have 8 as their base, so which ever value has the larger exponent (8^{4}) is the larger value. You will also come across instances of exponential comparisons where the bases differ such as: 5^{3} and 3^{6}. In these cases, you will need to work all the value that each expression represents to determine the actual basis for which to compare. 5^{3} = 5 x 5 x 5 = 125. That is the first value, now to see what we are comparing it to. 3^{6} = 3 x 3 x 3 x 3 x 3 x 3 = 729. So, in comparison of value 125 is less than 729 or it can be written as 5^{3} < 3^{6}. Always remember that the symbol of comparison always points toward the lesser value.

Exponents are the key behind a method that we use often to express values called scientific notation. Comparing the values of small numbers can be easy and the same is true of comparing larger numbers too. What can help us immensely in our quest is the use of exponents. An exponent is a method that is used to express a base ten unit on scale. Using this method, you can easily compare 2 very large numbers with a heck of a lot less writing. For instance, if we wish to compare numbers like 9,760,000,000 and 893,400,000,000, we will have to firstly convert the large number into exponential form. The numbers need to be converted in exponential form to have any chance of understanding the larger (or smaller number). The first number is 9.76 x 10^{9} and 8.934 x 10^{11}. In this example, the difference is visible, given that the exponent of the second number is greater than the first one. However, if take another example, like 23,630,000,000 and 24,300,000,000 and convert it in exponential forms with notations is 2.363 x 10^{10} and 2.43 x 10^{10} respectively. Now, the exponential values are the same in both numbers, so we'll look at the values before the exponent. 2.43 is greater than 2.363; thus, 2.43 x 10^{10} is greater than 2.363 x 10^{10}.