# Exponents, radicals, and scientific notation

Contents

Addition was nice. Multiplication was cooler. In the mood for a new operation that grows numbers even faster? Ever felt like expressing repeated multiplication with less writing? Ever wanted to describe how most things in the universe grow and shrink? Well, exponents are your answer!
This tutorial covers everything from basic exponents to negative and fractional ones. It assumes you remember your multiplication, negative numbers and fractions.

A strong contender for coolest symbol in mathematics is the radical. What is it? How does it relate to exponents? How is the square root different than the cube root? How can I simplify, multiply and add these things?
This tutorial assumes you know the basics of exponents and exponent properties and takes you through the radical world for radicals (and gives you some good practice along the way)!

If you're familiar with the idea of a square root, we're about to take things one step (dimension?) further with the cube root. This generally refers to finding a number that ,when cubed, is equal to the number that you're trying to find the cube root of!

Tired of hairy exponent expressions? Feel compelled to clean them up? Well, this tutorial might just give you the tools you need.
If you know a bit about exponents, you'll learn a ton more in this tutorial as you learn about the rules for simplifying exponents.

It's normally a bad idea to hang around with negative people or do negative things, but we think it's OK to associate with negative exponents. And fractional exponents are even more fun.
This idea will open up entirely new vistas to your mathematical life.

Scientists and engineers often have to deal with super huge (like 6,000,000,000,000,000,000,000) and super small numbers (like 0.0000000000532) . How can they do this without tiring their hands out? How can they look at a number and understand how large or small it is without counting the digits? The answer is to use scientific notation.
If you come to this tutorial with a basic understanding of positive and negative exponents, it should leave you with a new appreciation for representing really huge and really small numbers!

When people want to think about the general size of things but not worry about the exact number, they tend to think in terms of "orders of magnitude". This allows us to analyze and make comparisons between numbers very quickly, which allows us to make decisions about them quickly as well.

You already understand what scientific notation is. Now you'll actually use it to compute values and solve real-world problems.