## 1. Multiplying Polynomials with Same Base

### 1.1. The base stays the same and the exponents are added.

1.1.1. Example: 7^2+7^4=7^6

## 2. Dividing Polynomials with Same Base

### 2.1. The base stays the same and the exponents are multiplied.

2.1.1. Example: 7^5/7^2=7^3

## 3. Calculate the Power of a Power

### 3.1. The base stays the same exponents are multiplied.

3.1.1. Example: (3^3)^3=3^9

## 4. Variable

### 4.1. A letter that represents a value that can change.

4.1.1. Example: x

## 5. Term

### 5.1. A number, variable or exponent

5.1.1. Examples: 3, x, 3x, 3^3, 3x^3

## 6. Coefficient

### 6.1. The number part of a term.

6.1.1. Example: 8x, 8 is the Coefficient

## 7. Constant Term

### 7.1. A term that does not have any variables.

7.1.1. Example: 5

## 8. Degree

### 8.1. Of a single term

8.1.1. Sum of the degrees in the term.

8.1.1.1. Example: 3^5, 5 is the Degree of this Term

### 8.2. Of a polynomial

8.2.1. Highest degree in the polynomial.

8.2.1.1. Example: 7^2+8^4, 4 is the Degree of this Polynomial

## 9. Monomial

### 9.1. A polynomial with one term.

9.1.1. Example: 3x

## 10. Binomial

### 10.1. A polynomial with two terms.

10.1.1. Example: 2x+3

## 11. Trinomial

### 11.1. A polynomial with three terms.

11.1.1. Example: 1+7x-3x

## 12. Like Terms

### 12.1. Same variables and same exponents.

12.1.1. Example: 3x and 4x are Like Terms

## 13. Unlike Terms

### 13.1. Different variables or same variables with different exponents.

13.1.1. Example: 3x and 3y are Unlike Terms

## 14. Distributive Property

### 14.1. Simplifying an equation by combining like terms.

14.1.1. Example: 7x-3x=4x

14.1.2. Example: 3x (4x+2)=12x^2+6x

## 15. Dividing Polynomials with Different Base

### 15.1. Divide the constant terms and subtract the variables.

15.1.1. 10 a^5/5 a^2=2 a^3

## 16. Subtracting Polynomials

### 16.1. With same variable

16.1.1. Example: 7x^5-3x^5=4x^5

16.1.2. The variable stays the same and the constants are subtracted.

### 16.2. With different variable

16.2.1. You cannot subtract polynomials with different variables as both terms must be like terms in order to subtract.

## 17. Adding Polynomials

### 17.1. With Same Variable

17.1.1. Variable stays the same and the constants are added.

17.1.1.1. Example: 7x^5+6x^5=13x^5

### 17.2. With Different Variable

17.2.1. You cannot add two polynomials with different variables as both terms need to be like terms in order to be able to be added.

## 18. Constants With the Exponent of 0

### 18.1. Any constant to the exponent of 0 is equal to 1.

18.1.1. Example: 5^0=1