## Evaluating Negative Exponents

#### Aligned To Common Core Standard:

**Grade 8 Number System** - 8.EE.A.1

How to Evaluate Negative Exponents?
Evaluating exponents is one of the most common aspects of basic mathematics. Exponents are also called Indices or Powers. An exponent of any number indicates how many times will that number be multiplied with itself. For example.
8^{2} = 8 x 8 = 64
In other words, 8^{2} cam also be called the "8 to the second power", "8 squared" or "8 to the power 2".
So what to do when you have negative exponents. For example, something like 8^{-2} What does this mean?
Negative exponents are an inverse of the positive exponents, i.e., in positive exponents, the numbers get multiplied. When negative exponents are involved, it means that division operation will take place. For example:
5^{-3}= 1 ÷ 5 ÷ 5 ÷ 5 = 0.008 It can also be evaluated like this: 1 ÷ (5 x 5 x 5) = 1/5^{3} = 1/125 = 0.008. This well written series of worksheets and lessons will teach students how to determine the value of problems that include negative exponents.

### Printable Worksheets And Lessons

- Anatomy of Exponents Lesson- We spell it out for you. Positive exponents = multiply and negative = divide.

- Expressions with Negative Exponents Lesson - We show you multiple ways to solve this problem.

- Evaluating Negative Exponents Practice Worksheet 1 - There are two distinct skills that we work on here.

- Simplifying Expressions with Negative Exponents - It's all about viewing the problem from a far.

- Multiplication and Division with Negative Exponents - This is a slightly advanced skill for this level, but this should challenge your top students.

#### Evaluating Negative Exponents Practice Medium Difficulty

These are just one notch tougher than worksheet 1.

- Homework 2 - Apply the negative exponent rule and simplify.
- Homework 3 - Find the missing value.

#### Multiplication and Division with Negative Exponents

These really raise the bar with the advanced operations.

- Practice 2 - Eliminate the negative exponents and simplify. This a some real quality problems.
- Practice 3 - Here is the math Ninja, we have referenced before for you. He slices an dices math problems.

#### Upper Level Difficulty

Here is a two-step progression for students.

- Simplifying Advanced Expressions - This is a little more complicated. You will need to break this down in parts.
- Simplifying Expressions - These problems come in stacks. Start by simplifying anything that is possible for you.

### General Rules of Negative Exponents

When working with these types of problems there are some general rules that you should keep under consideration. These rules will help you keep a clear mental picture of what is going on here. When dealing with positive powers we understand that we are just multiplying the base number by itself the number of times indicated by the index. Just like the negative value is the opposite of a positive value, the same is true of the operations that result when dealing with exponents. When dealing with negative exponents the value of the index indicates how many times the base number is divided by itself. The general rule for raising a value to a negative power or index is that the numerator switches places with the denominator of the base value. In most cases this means that you place that same value over one. Which is another way to say that you just take the reciprocal of the base value.