# Basic Algebra/Polynomials/Exponents

## Vocabulary[edit]

**Base**: The number directly preceding an exponent

EX: a^{2} -> a is the base

**Exponent**: The number (written in superscript) used to express how many times a base is multiplied by itself

EX: a^{4} = a * a * a * a -> 4 is the exponent

EX: 4^{3} = 4 * 4 * 4 = 64 -> 3 is the exponent

## Lesson[edit]

Exponents are a simple way to represent repeated multiplication. For example a x a = a^{2}.
There are a few simple rules for exponents that help reduce very large problems to simple little ones. The rules are as follows:

1) The exponent of any number is always a one (1):
a = a^{1}

2) When we multiply the same base we add our exponenents:
a^{3} x a^{2} = a^{3 + 2} = a^{5}

3) When we divide the same base we subtract our exponents:
a^{6} / a^{4} = a^{6 - 4} a^{2}

4) When we raise a power to a power we multiply our exponents:
(a^{2})^{3} = a^{2 * 3} = a^{6}

5) When we raise a PRODUCT to a power we raise both parts of the product to the power:
(ab)^{3} = a^{3}b^{3}
[NOTE: This **ONLY** works with multiplication and **NOT** addition: (a + b)^{3} **≠** a^{3} + b^{3}]

6) When we raise a QUOTIENT to a power we raise both parts of the quotient to the power:
(a/b)^{2} = a^{2} / b^{2}
[NOTE: This **ONLY** works with division and **NOT** subtraction: (a - b)^{2} **≠** a^{2} - b^{2}]

## Example Problems[edit]

## Practice Games[edit]

## Practice Problems[edit]

Use `^`

for exponentiation and remember Order of Operations