In the world of real estate, the size of homes and buildings is measured in “square feet.” What does this terminology mean? One square foot equals 1 foot x 1 foot or 12 foot. The two in this expression is an exponent and it represents repeated multiplication. The various exponential properties that allow you to combine multiple exponents into a single one are the focus of this chapter. Once you’ve mastered these techniques, you’ll be able to evaluate what at first appear to be complicated exponential expressions.
This chapter begins with four important properties for combining exponents: Product of Powers, Power of a Product, Quotient of Powers, and Power of a Quotient. Negative, zero, and fractional exponents are discussed next. All these properties come together in the evaluation of exponential expressions. A way of representing very large and very small numbers more simply, known as scientific notation, is next covered. The chapter wraps up with discussion of geometric sequences and exponential functions, with an emphasis on real-world applications.