# Zero and Negative Exponents Worksheets

What happens when an exponent is equal to zero or is a negative value? If an exponent is zero, the overall value of the base with the exponent is equal to one. This can be helpful when solving larger problems because you can quickly simplify and value that has an exponent of zero to become one. Negative exponents on the other hand require you to evaluate them. If a value has a negative exponent that is the same as putting the positive value of the exponent as a denominator and the numerator as one. These worksheets and lessons help students learn how to handle exponents that are negative or zero in operations.

### Aligned Standard: 8.EE.A.1

- Working With Zeros Lesson- I know this can be pretty repetitive, but it can really help the concept hit home for students.
- Complex Negative Exponents Lesson - We start working with reciprocals and inverse problems.
- Guided Lesson - Plenty of space to work on these four problems.
- Guided Lesson Explanation - You will notice the numbers of different ways we tackle these problems.
- Zero Exponents Worksheet - Yes, ridiculously repetitive! But boy, is it effective!
- Negative Exponents Worksheet - A great practice page to work on these skills.

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

### Mixed Practice Sheets

You will find all the problems for this topic mixed about in here.

- Practice 1 - A whole bunch of different ways to approach these problems.
- Practice 2 - The zero goes by quickly.
- Practice 3 - Some fractions make their way towards you.
- Practice 4 - One over a negative exponent.

### Negative Exponents Practice Worksheets

More work for students.

- Practice 2 - Remember that your answers will only contain positive exponents.
- Practice 3 - The variable will go at you and then curve in a different direction.

### Zero Exponents Practice

These are for those days where you want to remind them of a simple topic or give them an easy quiz grade.

- Practice 2 - You might catch on after the third problem.
- Practice 3 - The second go around. See if it helps you improve.

### What is the Value of Zero Exponents or Negative Exponent Value?

Let us get the easiest part of this question out of the way first. It does not matter what your base number if the value of the exponent is zero, the overall value of that expression is equal to one. The base number can be positive or negative, that does not matter. Anything to the zero power is equivalent to 1.

If a base number is raised to a negative exponent the final value gets a bit more complex, because it moves us to the inverse of the number itself. What this means is that you place the exponent under 1 (as a fractional value) and remove the negative value from the exponent. This process of placing the 1 over the value is considered taking the reciprocal of that value. In terms of a formula it would look like a^{-b} = 1/ a^{b}.

### Real World Applications

These values are found in different forms. Zero exponents are more often than not found only in theoretical calculations depending on the nature of the substance or material you are considering working with. Negative exponents are pretty common in many different forms of measurement that use scientific notation. They help us signify very small quantities of these measurements as a negative tens place gives you a small decimal value.