1. Exponents and Order of Operations Section 1.7

2. 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 exponent base 2 Martin-Gay, Prealgebra, 5ed

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

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

5. Reading Exponential Notation... 4  4  4 = 4  4  4  4 = is read as “four to the third power” or “four cubed.” is read as “four to the fourth power.” 5 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 = 2 1 and 7 = 7 1. 6 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. 3 5 = 3 3 3 3 3 = 243 7 Martin-Gay, Prealgebra, 5ed

8. Helpful Hint An exponent applies only to its base. For example, Don’t forget that 2 4 is not 2 4. 2 4 means repeated multiplication of the same factor. 4 2 3 means 4 2 2 2. 2 4 = 2 2 2 2 = 16, whereas 2 4 = 8 8 Martin-Gay, Prealgebra, 5ed

9. 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. Order of Operations 9 Martin-Gay, Prealgebra, 5ed