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Fundamentals of Algebra Chu v. Nguyen Integral Exponents Exponents If n is a positive integer (a whole number, i.e., a number without decimal part) and x is a number, then The number x is called the base and n is called the exponent. The most common ways of referring to are “ x to the nth power,” “ x to the nth,” or “the nth power of x.” Integral Exponents (cont.) For any non-zero number x and a positive integer n and Note: is not defined and Rules Concerning Integral Exponents Following are five rules in which m and n are positive integers: Rule 1: ; for example, Rule 2: ; for example or Rules Concerning Integral Exponents (Cont.) Rule 3: ; for example or Rule 4: ; for example or Rule 5: ; for example or Basic Rules for Operating with Fractions Since dividing by zero is not defined, we assume that the denominator is not zero. Following are the eight basic rules for operating with fractions. Rule 1: ; for example Rule 2: ; for example Rule 3: ; for example Basic Rules for Operating with Fractions (cont.) Rule 4: ; for example Rule 5: ; for example Rule 6: ; for example Basic Rules for Operating with Fractions (cont.) Rule 7: ; for example Rule 8: ; for example Notes: a*b +a*x may be expressed as a(b + x) a*b + 1 may be written as a(b + ), and m*x – y may be expressed as m(x - ) Square Root Generally, for a>0 , there is exactly one positive number x such that , we say that x is the root of a, written as for When n = 2, we say that x is the square root of “a” and is denoted by or or For example: or Practices Carrying out the following operations: 24 ; 2-2 ; 2322, ; 252-5 ; and (2x3)5 ; ; ; and 3. 4. 5. n m n m x x x + = n x 1 0 ) 2 ( 2 2 2 = = = - + - x x x x 1 0 = x 0 0 n n n x x x x = = + 0 0 n n x x 1 = - 3 2 ...
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Properties Of Exponents
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