## Properties of Integer Exponents

#### Aligned To Common Core Standard:

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

Rules of Integer Exponent Operations
Here the rules that students need to follow in regards to the integer exponent operations along with some of the examples.
**Zero-Exponent Rule** - a^0 = 1, this rule states that any number raised to the power of zero is equal to 1
**Power Rule** - This rule is also called power to power rule: (am)n = amn. According to this rule, when you raise a power to another power, you have to multiply the exponents. Many other rules are associated with the power rule. For example, product-to-powers rule or the quotient to power rule.
**Negative Exponent Rule** - This rule states that negative components, when shifted their position from denominator to numerator, change their sign. If the sign is negative in the denominator, then they turn positive when they become numerator.
**Product Rule** - am ∙ an = am + n. This rule states that when two exponents are being multiplied with the same base, the base remains the same as the powers are added.
**Quotient Rule** -This rule states that when two exponents of the same base are divided with each other, the base remains the same; the powers of the two are subtracted with each other. It is very much familiar to the fraction reduction. When the powers are subtracted, the answers are placed in the denominator or the numerator, depending on where the higher power has been located.
This collection of worksheets and lessons help students understand how to work with exponents in a variety of different scenarios.

### Printable Worksheets And Lessons

- Multiply Exponents Step-by-Step
Lesson- Not only that! There are negative exponents. They're
on fire while a wake boarder jumps them! Too over the top?

- Guided Lesson - It's
all about simplifying exponents. There is also some division and
multiplication of exponents along the way too.

- Guided Lesson Explanation
- The division problems make really small numbers and multiplication
just the opposite.

- Independent Practice -
This work sheet has appeared at two National Conferences already.
Here I am just thinking that the bat is cute!

- Matching Worksheet
- I know that this can be a tough sheet for some kids. They often
get choice "c" and "d" confused. Heads up!

- Exponents to Numbers Five Pack - Put the exponents in numerical form and then compare the values of the exponents.

#### Homework Sheets

Multiplication and division of exponents followed by exponents of exponents.

- Homework 1 - This is a base with a negative exponent. We can turn it into a positive exponent by using a little math ninja move.
- Homework 2 - If the base is in (a^x)^y form, the two exponents should be multiplied.
- Homework 3 - When we have the same base to be multiplied with different exponents a^x times a^y, the exponents must be added.

#### Practice Worksheets

We follow the same progression in the practice sheets as we did with the homework.

- Practice 1 - Simplify the expressions.
- Practice 2 - Remember what to do with zero and one as exponents.
- Practice 3 - Remember when you should add and subtract exponents.

#### Math Skill Quizzes

Once again, we stick with the progression. The quiz problems are standard questions that you will see often.