Powers, Exponents, and Roots
Introduction and Summary
Exponents play a large role in mathematical calculations. This chapter provides an introduction to the meaning of exponents and the calculations associated with them. Since exponents are used abundantly in all of mathematics, the basics taught in this chapter will become important building blocks for future knowledge.
The first section will explain the fundamentals of exponents, and explore squares, cubes, and higher order exponents. This section will explain how to square and cube numbers, as well as how to recognize a perfect square.
The second section will focus on exponents applied to specific types of numbers--namely, negative numbers, decimals, and fractions. Here, we will learn how to raise these base numbers to any power.
The third section will explore calculations in which the exponent is negative. It will explain the meaning of a negative exponent and how to evaluate expressions that contain negative exponents. It will also show the importance of negative exponents to the base ten system while discussing how write out any terminating decimal as a sum of single-digit numbers times powers of ten.
The fourth section will deal with roots--square roots, cube roots, and higher order roots--and fractional exponents. This section will explain what a root is and how to find a root if the answer is rational. It will also explain why we cannot take the square root (or any even root) of a negative number. This section will also explain how to raise a number to a fractional power.
The fifth section will deal with roots that are not easy to find. It first shows how to simplify a square root to make calculations easier, and it then shows how to find an approximate decimal value for a square root.
Overall, this chapter offers an introduction to exponents for those readers who have never been exposed to them, and an opportunity to sharpen knowledge to those who have. Exponents will play an important role in pre-algebra during area calculations. They will also be very important in future mathematical endeavors, including algebra, geometry, calculus, and higher mathematics.