# Welcome to the Planet of Exponents!

### Learn about ways to learn all the laws of our planet!

## Greetings, from the Planet of Exponents!

## Welcome tourists to the Planet of Exponents!

Here on our planet, we follow the guidelines of the 7 laws of exponents, hence the name. To help you all on your way and to stay out of trouble, read on to learn about the 7 laws of exponents: the product rule, quotient rule, the power rules I and II, the negative exponents I and II, and zero exponents!

## The laws of our planet:

## Now lets learn about each exponent!

## PRODUCT RULE!

*The same base, just*

**add**the exponents!This means...

To multiply two exponents with the same base, you keep the base and add the powers.

Commonly broken rules:

- Often the exponents are multiplied by each other instead of added.
- instead of
**adding the exponents of X to the 3rd x X to the 6th (3+6=9; X to the 9th)**, they multiply the powers (3x6=18; X to the 18th).

## Quotient Rule!

*The same base, just*

**subtract**the exponents!This means...

To divide two exponents with the same base, you keep the base and subtract the powers.

Commonly broken rules:

- Often the exponents are divided by each other instead of subtracted.
- Instead of
**subtracting the exponents of****X to the 6th / X to the 3rd (6-3=3; X to the 3rd)**, they divide the powers (6/3=2; X to the 2nd).

## Power Rule I!

*Power raised to a power multiply exponents!*

This means...

That you just multiply the exponents and keep the base.

Commonly broken rules:

- Sometimes the exponents are added instead of being multiplied.
- Instead of
**multiplying the exponent through the parenthesis ( (X3)3 = X9; X to the 9th)**, they add the powers like a product rule. ( (X3)3 = X6; X to the 6th).

## Power Rule II!

*Product to power distribute to each base!*

This means...

Distribute the power to each product to simplify your equation.

Commonly broken rules:

- Sometimes the exponents are instead of multiplying the exponents.
- Instead of
**multiplying the exponent through the parenthesis ( (2X3)3 = 8X9; 8X to the 9th)**, they forget to use the power to the first like term ( (2X3)3 = 2X9; 2X to the 9th).

## NEGATIVE EXPONENT I!

*Flip and change sign to positive!*

This means...

Reciprocate your equation over one to change your negative exponent to positive.

Commonly broken rules:

- Often the negative exponent is applied to everything in the problem, not just the variable that has the negative exponent.

**Incorrect example:** 3a^ -5 = 1/ 3a^5 **Correct example: **3a^ -5 = 3/ a^-5

## NEGATIVE EXPONENT II!

*Flip and change sign to positive!*

This means...

Reciprocate your equation to change your equation under one to over one to make your exponents positive.

Commonly broken rules:

- Often the problem is not reciprocated so that the exponent is not negative.

**Incorrect example: ** = 1/ a^ -2 = 1/ a^ 2 **Correct example: **1/ a^ -2 = a^2

## Multiple Rule Problems

*In order to solve multiple rule equations you must follow these 4 easy steps!*

- Get rid of any 0 exponents
- Add the exponent of 1 to any plain variables
- Distribute to get rid of parentheses
- Combine like bases

**Don't forget to put your final answer in alphabetical order!**

Sometimes these 4 steps are forgotten and the simplifying of the problem is incorrect or out of order. Following these steps will help you to correctly solve your problem!

## Consequences:

If these laws are to be broken, here is the consequences on the Planet of Exponents...

**1st offense: Tutoring on the laws of exponents.****2nd offense: Drink a bottle of ketchup****3rd offense: Wear a pink easter bunny costume for 3 days.****4th offense: Eat 4 habanero/ jalapeno peppers.**