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A.2 Exponents and Radicals

Appendix and RadicalsA11 Exponential NotationIf is a real number and is a positive integer, thenn factorswhere is the exponentandis the expression is read tothe th power. naananan a a a .. anaWhatyou should learn Use properties of Exponents . Use scientific notation to represent real numbers. Use properties of Radicals . Simplify and combine Radicals . Rationalize denominators andnumerators. Use properties of rational should learn itReal numbers and algebraicexpressions are often writtenwith Exponents and Radicals . Forinstance, in Exercise 105 on pageA22, you will use an expressioninvolving rational Exponents to find the time required for a funnel to empty for differentwater and ExponentsRepeated multiplicationcan be written in exponential MultiplicationExponential Form 2x 4 2x 2x 2x 2x 4 3 4 4 4 a5a a a a aAn exponent can also be negative. In Property 3 below, be sure you see how touse a negative of ExponentsLet and be real numbers, variables, or algebraic expressions, and let and be integers.

A14 Appendix A Review of Fundamental Concepts of Algebra Radicals and Their Properties A square rootof a number is one of its two equal factors.For example, 5 is a square root of 25 because 5 is one of the two equal factors of 25. In a similar way, a cube rootof a number is one of its three equal factors, as in Some numbers have more than one nth root.. For example, both 5 and

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