Easy Algebra Step-by-Step

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7 Rules for Exponents

In Chapter 4, you learned about the various types of exponents that you

might encounter in algebra. In this chapter, you learn about the rules for

exponents—which you will fi nd useful when you simplify algebraic expres-

sions. The following rules hold for all real numbers x and y and all rational

numbers m, n, and p, provided that all indicated powers are real and no

denominator is 0.

Product Rule

Product Rule for Exponential Expressions with the Same Base

xxmnx =xmn+

This rule tells you that when you multiply

exponential expressions that have the same base,

you add the exponents and keep the same base.

Problem Simplify.

a.xx^23 x

b. xy^25 y

c. xx^27 x yy^35 y

P

If the bases are not the same, don’t

use the product rule for exponential

expressions with the same base.