# Evaluating Numerical Expressions with Exponents Worksheets

We have already learned the order of operations when evaluating expressions. One of those big operations that we have come across in PEMDAS is the "E" part which stands for exponents. As you can see, they are evaluated just after the parenthesis and before multiplication, but they are a vital part of solving expressions. Students should be confident when they are breaking down these calculations and working with exponents. An exponent simply tells us how many times we multiply that value by itself. Some students confuse this with multiplying the exponent and the root number. The quicker we realize that 4^{3} is equal to: 4 x 4 x 4, the better. These worksheets and lessons will baby step you into first evaluating exponents and then open the big picture for you and see how to manipulate them in complex expressions.

### Aligned Standard: Grade 6 Expressions and Equations - 6.EE.A.1

- Exponent Conversion Step-by-step Lesson- Convert repeated multiplication to exponent use.
- Guided Lesson - We cover simple exponent conversion and then include it in sums and differences.
- Guided Lesson Explanation - I forgot how hard exponents were to explain with just writing.
- Practice Worksheet - I only dedicated 20% of the problems to using exponents in operations. Everything else is just exponent conversion.
- Making Exponents Five Pack - Convert everything you see to exponents.
- Evaluate Expressions with Fractional Exponents Five Pack - Some pretty difficult exponents to work with here guys.
- Writing Exponents Five Pack - Everything is in standard form or an equation. Write those as exponents.
- Matching Worksheet - One of the answers in this one is huge!

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

### Homework Sheets

Start with expanding basic exponents then move on to products and sums with exponents.

- Homework 1 - The exponent of a number tells you how many times it should be multiplied by itself.
- Homework 2 - Write your answers in expanded form.
- Homework 3 - Expand & evaluate 3
^{8}

### Practice Worksheets

Only the first sheet includes the use operations with the exponents.

- Practice 1 - Evaluate some terms and then expand them.
- Practice 2 - Expanding Exponents
- Practice 3 - We use much larger values here.

### Math Skill Quizzes

I revised these several times since the wording on standard has been changed each year.

- Quiz 1 - Write in exponential form.
- Quiz 2 - Write your answers in expanded form.
- Quiz 3 - Check the expressions multiple times.

### What Are Exponents?

The power or exponent of a number is the result of the multiplication of this number by itself a certain number of times according to the exponent. Examples: 2^{2} = 2 × 2 = 4, 2^{3} = 2 × 2 × 2 = 8, Do not confuse with multiplication: 2^{3} = 2 × 2 × 2 = 8, 2 × 3 = 2 + 2 + 2 = 6

**Exponent Power** - In the general case: a^{n} reads "the variable a has exponent n" or "has the power n". Both terms are equivalent. For example, 6^{8} reads " six exponent eight " or "six to the power eight".

A power with an exponent equal to two can also be said "squared": 7^{2} reads "seven squared".

A power with an exponent equal to three can also be called "cube": 7^{3} reads "seven cubed".

**The powers of 10** - The powers of 10 are special cases. They make it possible to write large numbers.

10^{2} = 10 × 10 = 100 (two zeros after 1), 10^{3} = 10 × 10 × 10 = 1,000 (three zeros), 10^{4} = 10 × 10 × 10 × 10 = 10,000 (four zeros)

Note that the number of zeros present in the power corresponds to the exponent. This is handy for representing a number. Thus, one million (1,000,000) can be written 10^{6}. This only works for powers of 10.

### How Do We Evaluate Expressions That Contain Exponents?

We need to remember that when we are evaluating any expression the order of operations that we have previously described as PEMDAS still hold true.

We will use the example expression: 4x^{2} + 5. We might be asked to evaluate this expression when x = 3.

To properly evaluate this, we will follow a simple strategy:

**Step 1) Plug in** - We would just replace the variable x with the value that we were given for it. So now the expression will be rewritten as:

4(3)^{2} + 5.

**Step 2) Evaluate the Exponent** - When 3 is raised the second power that is the same thing as saying: (3)^{2} = 3 x 3 = 9. We can now rewrite our expression as:

4(9) + 5.

**Step 3) Order of Operations** - Following PEMDAS, multiplication comes before addition so we will multiply 4 and 9 for a value of 36. We can rewrite it one last time as:

36 + 5 = 41 (I'd write another step for addition, but that just seem like overkill.)