1. © 2010 Pearson Prentice Hall. All rights reserved 1.7 Exponents and Order of Operations

2. Martin-Gay, Prealgebra, 6ed 22 © 2010 Pearson Prentice Hall. All rights reserved 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 Exponents

3. Martin-Gay, Prealgebra, 6ed 33 © 2010 Pearson Prentice Hall. All rights reserved 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 Exponential Notation

4. Martin-Gay, Prealgebra, 6ed 44 © 2010 Pearson Prentice Hall. All rights reserved 4 = 4 1 4  4 = 4 2 is read as “four to the first power.” is read as “four to the second power” or “four squared.” Reading Exponential Notation

5. Martin-Gay, Prealgebra, 6ed 55 © 2010 Pearson Prentice Hall. All rights reserved 4  4  4 = 4 3 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.” Reading Exponential Notation

6. Martin-Gay, Prealgebra, 6ed 66 © 2010 Pearson Prentice Hall. All rights reserved 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. Helpful Hint

7. Martin-Gay, Prealgebra, 6ed 77 © 2010 Pearson Prentice Hall. All rights reserved 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 Evaluating Exponential Expressions

8. Martin-Gay, Prealgebra, 6ed 88 © 2010 Pearson Prentice Hall. All rights reserved 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 Helpful Hint

9. Martin-Gay, Prealgebra, 6ed 99 © 2010 Pearson Prentice Hall. All rights reserved 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars, starting with the innermost set. 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