Exponents and Order of Operations

1. Section 1.7 Exponents and Order of Operations

2. exponent base An exponent is a shorthand notation for repeated multiplication. 3 • 3 • 3 • 3 • 3 3 is a factor 5 times Using an exponent, this product can be written as Martin-Gay, Prealgebra, 5ed

3. exponent base This is called exponential notation. The exponent, 5, indicates how many times the base, 3, is a factor. Read as “three to the fifth power” or “the fifth power of three.” 3 • 3 • 3 • 3 • 3 3 is a factor 5 times Martin-Gay, Prealgebra, 5ed

4. Reading Exponential Notation 4 = is read as “four to the first power.” 4  4 = is read as “four to the second power” or “foursquared.” Martin-Gay, Prealgebra, 5ed

5. Reading Exponential Notation . . . 4  4  4 = is read as “four to the third power” or “four cubed.” 4  4  4  4 = is read as “four to the fourth power.” Martin-Gay, Prealgebra, 5ed

6. Helpful Hint Usually, an exponent of 1 is not written, so when no exponent appears, we assume that the exponent is 1. For example, 2 = 21and 7 = 71. Martin-Gay, Prealgebra, 5ed

7. To evaluate an exponential expression, we write the expression as a product and then find the value of the product. 35 = 3 • 3 • 3 • 3 • 3 = 243 Martin-Gay, Prealgebra, 5ed

8. Helpful Hint An exponent applies only to its base. For example, 4• 23means 4 • 2 • 2 • 2. Don’t forget that 24 is not 2 • 4. 24 means repeated multiplication of the same factor. 24 = 2• 2 • 2 • 2 = 16, whereas 2 • 4 = 8 Martin-Gay, Prealgebra, 5ed

9. Order of Operations 1. Perform all operations within grouping symbols such as parentheses or brackets. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right. Martin-Gay, Prealgebra, 5ed