Technical Mathematics, Sixth Edition

Chapter 13. Exponents and Radicals

OBJECTIVES When you have completed this chapter, you should be able to Use the laws of exponents to simplify and combine expressions having integral exponents, by hand or by calculator. Simplify radicals by removing perfect powers, by rationalizing the denominator, and by reducing the index. Add, subtract, multiply, and divide radicals. Solve radical equations, manually or by calculator.

We introduced exponents and gave the laws of exponents in our "Introduction to Algebra" chapter. We review those laws here, give more advanced examples of their use, with applications, and show how to manipulate expressions having exponents by calculator.

Next we make a strong connection between exponents and radicals, and show how to simplify, add, subtract, multiply, and divide radical expressions. We did some calculation of roots in Chapter 1, but with only numbers under the radical sign. Here we show how to handle expressions with literals under the radical sign. The ability to manipulate both exponents and radicals is needed to work with many formulas found in technology.

Finally we add another kind of equation to our growing list, the radical equation. As with quadratics, we start with methods of solution that we already know, solution by graphing and by calculator. This is followed by methods for an algebraic solution, and of course, applications. For example, the natural frequency f_n of the weight bouncing at the end of a spring, Fig. 13-1, is given by ...