# Welcome to 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!

## 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:

• 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

## ZERO EXPONENT!

Anything to the zero power (except 0) is one!

Commonly broken rules:

• Sometimes equations to the power of zero are thought to be zero.
• (i.e. instead of 4 to the 0 power equals 1 (4 to the 0 power = 1), they mistake it as 4 to the 0 power (4 to the 0 power = 4).

## Multiple Rule Problems

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

1. Get rid of any 0 exponents
2. Add the exponent of 1 to any plain variables
3. Distribute to get rid of parentheses
4. Combine like bases

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.