# Laws of Exponents

## The product of a power property and The power of a power property

When ever you have bases with the same number you always add the exponents together. Like so, Ex: (5^3)(5^9)= 5^12

If you have an exponent that is out side your parentheses you will multiply that exponent by the exponent that is in the parentheses. Ex: (4^4)^9= 4^36

## The power of product property and The quotient of powers property

If you have a base with and x right right next to it in parentheses. Outside of the parentheses there is an exponent, you will distribute the exponent to the base and the x. Ex: (3x)^4= 3^4 x^4

When ever you have bases with the same number that are over top of each other with an exponent you will subtract both of the exponents. Like so, Ex: 2^6/2^1= 2^5

## The power of a quotient property and Definition of negative exponents

If you have a fraction as your base in parentheses and an exponent outside of the parentheses you must distribute the exponent to the numerator and the denominator. Then divide the fraction you have just made to create your answer.

Ex: (3/4)^2= 3^2/4^2= .5625

You cannot have a negative exponent, therefore you must put the base and exponent into a fraction. Ex: 1^-4= 1/1^4

## Definition of zero exponent and Explanation of exponential growth/decay

Zero exponent: Anything that has a zero as a exponent will always be 1. Doesn't matter what the base is. Ex: 4^0=1, 7^0=1, ect.

Exponential growth/decay: Exponential growth occurs when the growth rate of the value of the mathematical function is drastically increased. Exponential decay works the same way when the growth rate is negative.

## An explanation of fractional exponents

When you have a fraction at as your exponent you must change it so that your denominator is cubing your base, your numerator will square the cubed root. Ex: 25^3/5= (5√25)^3= (5)^3=125