Exponents help us write repeated multiplication with little effort. In this chapter, you will learn how to simplify, multiply and divide expressions containing exponents. Exponents also allow us to express very large and very small numbers without a lot of zeros and confusion, using so-called scientific notation. Scientists and engineers make use of exponents regularly to keep track of the place value of numbers that they are working with to make calculations. For example, [latex]1,000,000[/latex] is written as [latex]{1}\times{10}^{6}[/latex] and .00001 becomes [latex]{1}\times{10}^{-4}[/latex].

What if you want to “undo” an exponent? For example if you square [latex]6[/latex] to get [latex]36[/latex], how can you get back to [latex]6[/latex]? The complementary operation of exponentiation is a radical (aka. root). The root of a number x is another number, which when multiplied by itself a given number of times, equals x.

In this chapter, you’ll learn how to:

• Simplify expressions using the rules of exponents
• Convert between decimal and scientific notation of a number
• Multiply and divide numbers expressed in scientific notation
• Solve application problems involving scientific notation
• Simplify, evaluate and estimate square roots