1. ALGEBRA READINESS LESSON 2-6 Warm Up Lesson 2-6 Warm Up

2. ALGEBRA READINESS LESSON 2-6 Warm Up Lesson 2-6 Warm Up

3. ALGEBRA READINESS “Positive Exponents” (2-6) What does “simplify” mean? What is a a “base” number, “exponent”, and “power”? Why is there a certain order to simplifying expressions with multiple (more than one) operations (like +, -, x, ÷) simplify: to make as simple as possible (in other words, what’s the answer) exponent : a shorthand way to show repeated multiplication of a base number by showing how many times to multiply the base number by itself using a superscript (a little number at the top right of the base number) power: includes both the base number and the exponent (For example, you read 5 4 as “five to the fourth power” and 5 7 as “five to the seventh power”. Exponents of 2 and 3 have special names – “squared” and “cubed”. For example, 5 2 is read as “five squared” and 5 3 is read as“five cubed”) If you simplify an expression in any order you want, you’ll come up with different answers. Example:

4. ALGEBRA READINESS “Positive Exponents” (2-6) What is the correct order of operations? To remember the order of operations mathemeticians have agreed upon, remember PEMDAS or “Please Excuse My Dear Aunt Sally” 1.Parenthesis: Do operations within parenthesis () first. If there are parenthesis with parenthesis, such as [()] or {[()]}, work from the inside parenthesis to the outside parenthesis. 2.Exponent: Powers 3.Multiplication and Division from left to right. 4.Addition and Subtraction from left to right. Fractions: Fraction bars act as grouping symbols. For expressions like, do the calculations above and below the fraction bar before simplifying the fraction itself. Substitution: Always substitute (replace letters with numbers if you know them) before using PEMDAS.

5. ALGEBRA READINESS Write 2 2 2 7 7 using exponents. 2 is multiplied by itself 3 times and 7 is multiplied by itself 2 times. 2 3 7 2 Positive Exponents LESSON 2-6 Additional Examples

6. ALGEBRA READINESS (–2) 6 (–2) 6 = (–2)(–2)(–2)(–2)(–2)(–2) The base –2 is multiplied 6 times. Simplify the expression: Positive Exponents LESSON 2-6 Additional Examples (4)(–2)(–2)(–2)(–2) Use PEMDAS. (–8)(–2)(–2)(–2) (16)(–2)(–2) (–32)(–2) 64

7. ALGEBRA READINESS 24 – (8 – 1.2  5) 2 Substitute 5 for x. Evaluate the expression 24 – (8 – 1.2 x) 2 for x = 5. Work inside the grouping symbols. Multiply first. 24 – (8 – 6) 2 24 – (2) 2 Subtract inside the parentheses. 24 – 4 Simplify the power. 20 Subtract. Positive Exponents LESSON 2-6 Additional Examples

8. ALGEBRA READINESS Simplify 32 + 6 2 – 14 3. 32 + 6 2 – 14 3 = 32 + 36 – 14 3 Exponent: 6 2 = 6 6 = 36. = 32 + 36 – 42Multiply 14 and 3. = 68 – 42 Add and Subtract in order from left to right. = 26 Add and Subtract in order from left to right Positive Exponents LESSON 2-6 Additional Examples

9. ALGEBRA READINESS Evaluate 5x + 3 2 ÷ p for x = 2 and p = 3. 5x + 3 2 ÷ p = 5 2 + 3 2 ÷ 3Substitute 2 for x and 3 for p. = 5 2 + 9 ÷ 3Exponent (Power). = 10 + 3Multiply and Divide from left to right. = 13Add and Subtract from left to right. Positive Exponents LESSON 2-6 Additional Examples

10. ALGEBRA READINESS Find the total cost of a pair of jeans if the price is $32 and the sales tax rate is 8%. total cost original price sales tax C=p+r p sales tax rate (in fraction or decimal form) C = p + r p = 32 + 0.08 32Substitute 32 for p. Change 8% to 0.08 and substitute 0.08 for r. = 32 + 2.56Multiply first. = 34.56Then add. The total cost of the jeans is $34.56. Positive Exponents LESSON 2-6 Additional Examples

11. ALGEBRA READINESS Write each expression using an exponent. 1.6 62.8 8 8 Simplify each expression. 3.5 4 4.3.2 2 5.2 3 + (10 – 5)6.3 2 (9 – 2) + 1 6262 8383 62510.24 1364 Positive Exponents LESSON 2-6 Lesson Quiz