Exponents

Just like multiplication is a repitition of addition, exponents are a repitition of multiplication. An exponent looks like this: b^x. b would be the base , and x would be the exponent. In 5², 5 is the base and 2 is the exponent.

What this all means is: you take the base, and you multiply it against it self as many times as the exponent. 2⁴ would be 2 ⋅ 2 ⋅ 2 ⋅ 2 = 16. 5³ = 5 ⋅ 5 ⋅ 5 = 125. If the exponent is 2, then you say "squared". If it is 3, you say "cubed". If its bigger than that then you just say "to the x^th power". This all assumes that the exponent isn't 0. If it is, in fact, 0, the whole thing comes out to 1. That's right. 5⁰ = 1. 19⁰ = 1. (22² + (9*5))⁰ = 1. That's just the way things are.

There are a few basic laws of exponents:

Multiplying exponents: b^a + b^q. This means p² + p⁵ = p⁷. 5² + 5⁴ = 5⁶ = 15625

Power of a power: (b^s)^t = b^st. (5²)³ = 5⁶ = 15625

Power of a product: (ab)^c = a^cb^c.

Power of a fraction: (a/b)^q = a^q/b^q

Division of powers: b^q/b^m = b^q-m. 5³/5¹ = 5^3-1 = 5² = 25.

Simple, huh?