1. Definition of Let b represent any real number and n represent a positive integer. Then, n factors of b

2. Evaluating Expressions with Exponents ExpressionBaseExponentResult 6²62(6)(6) = 36 (-½)³-½3(-½)(-½)(-½) = - 0.8⁴0.84(.8)(.8)(.8)(.8) =.4096

3. Evaluating Expressions with Exponents 5 is the base to the exponent 4 Multiply -1 times four factors of 5 Parentheses indicate that -5 is the base to the exponent 4. Multiply four factors of -5 = (-5)(-5)(-5)(-5) = 625

4. Substitute a = 2 Evaluate each expression for a = 2 and b = -3 Use parentheses to substitute a number for a variable. = 5 ( )² 2 Simplify 2 = 5(4) = 20

5. Substitute a = 2 Evaluate each expression for a = 2 and b = -3 Use parentheses to substitute a number for a variable. = [5( )]² 2 Simplify inside the parentheses first 2 = (10)² = 100

6. Substitute a = 2 b = -3 Evaluate each expression for a = 2 and b = -3 Use parentheses to substitute a number for a variable. = 5( ) ( )² 2 Simplify inside the parentheses first 2 = 5(2)(9) = 100 -3 multiply Tip: In the expression 5ab² the exponent, 2 applies only to the variable b. The constant 5 and the variable a both have an implied exponent of 1.

7. Substitute a = 2 b = -3 Evaluate each expression for a = 2 and b = -3 = (a + b )² 2 Simplify inside the parentheses first 2 = [(2) + (-3)]² = (-1)² -3 = 1 Avoiding Mistakes: Be sure to follow the order of operations. It would be incorrect to square the terms within the parentheses before adding.

8. Multiplication of Like Bases Assume that a≠ 0 is a real number and that m and n represent positive integers. Then, Property 1

9. Division of Like Bases Assume that a ≠ 0 is a real number and that m and n represent positive integers such that m > n. Then, Property 2:

10. Simplifying Expressions with Exponents (w∙w∙w)(w∙w∙w∙w) Add the exponents (2∙2∙2∙2∙2∙2∙2) Add the exponents ( the base is unchanged).

11. Simplifying Expressions with Exponents (t∙t∙t∙t∙t∙t) (t∙t∙t∙t) Subtract the exponents 5∙5∙5∙5∙5∙5 5∙5∙5∙5 Subtract the exponents ( the base is unchanged).

12. Simplifying Expressions with Exponents Subtract the exponents Note that 10 is equivalent to 10¹ Add the exponents in the denominator ( the base is unchanged). Add the exponents in the numerator ( the base is unchanged). Subtract the exponents Simplify

13. Simplifying More Expressions (3p²q⁴)(2pq⁵) Apply the associative and commutative properties of multiplication to group coefficients and like bases =(3∙2)(p²p)(q⁴q⁵) Add the exponents when multiplying like bases. Simplify

14. Simplifying More Expressions Group like coefficients and factors. Subtract the exponents when dividing like bases. Simplify