Algebra Help - Education Online
Algebra real numbers, formulas, linear and quadratic functions, exponent properties, products and factoring tutoring Properties of Exponents
You have seen the basic principles for addition and multiplication of real numbers. From these basic principles, other principles can be derived. Note some properties of exponents that follow easily from the basic principles. Notice, for example, that 22 - 23 = (2 - 2) - (2 - 2 - 2) = 4 - 8 = 32 and that 25 = 2 - 2 - 2 - 2 - 2 = 32 In fact, it is easy to prove the following principle: x x2 - x3 = x5 This principle tells you that for each real number 'x', the product of 'x2' by 'x3' is 'x5'. [Notice that 2 + 3 = 5.] Note also, for example, that
These examples suggest the following principles that are easily proved to be consequences of the basic principles: [Notice that 5 - 2 = 3.] The principles suggest methods you may use to solve problems like the following without using pencil and paper:
You may, of course, check the answers by computing. For example, in the last problem we have: Continue Algebra Help with ....• Real Numbers • Formulas, Functions, Graphs • Linear Functions • Quadratic Functions • Functions of Higher Degree • Properties of Exponents • Products and Factoring • Quadratic Equations • Solving Problems • Algebra Fundamentals |