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Exponents, Complex Fractions, and
the Order of Operations Agreement
Exponents : Recall that an exponent indicates the repeated multiplication of the same factor. For example:
The exponent, 5, indicates how many times the base, 3, occurs as a factor in the multiplication.
The base of an exponential expression can be a fraction, for example:
Evaluate :
Write each factor as many times as indicated by the exponent.
Multiply. The product of two negative numbers is positive.
Write the product in simplest form.
Evaluate: x^3 when x = 2.
Replace x with 2.
= (2.5) 3
Multiply.
= 7.
COMPLEX FRACTIONS: A complex fraction is a fraction whose numerator or denominator contains one or more fractions.
Examples: ,
is a division problem and may be rewritten as :
ORDER OF OPERATIONS AGREEMENT:
Recall the following steps in the order of operations: 1.) Do all operations in groupings ( note: fraction bars act as a grouping ). 2.) Simplify exponents. 3.) Perform multiplication and division operations, as they occur, from left to right. 4.) Perform addition and subtraction operations, as they occur, from left to right.
