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LESSON 2-6Warm Up Lesson 2-6 Warm Up

ALGEBRA READINESS

LESSON 2-6Warm Up Lesson 2-6 Warm Up

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 54 as “five to the fourth power” and 57 as “five to the seventh power”. Exponents of 2 and 3 have special names – “squared” and “cubed”. For example, 52 is read as “five squared” and 53 is read as“five cubed”)

If you simplify an expression in any order you want, you’ll come up with different answers.

Example:

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“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.

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Write 2 • 2 • 2 • 7 • 7 using exponents.

2 is multiplied by itself 3 times and 7 is multiplied by itself 2 times.

23 • 72

Positive ExponentsLESSON 2-6

Additional Examples

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(–2)6

(–2)6 = (–2)(–2)(–2)(–2)(–2)(–2) The base –2 ismultiplied 6 times.

Simplify the expression:

Positive ExponentsLESSON 2-6

Additional Examples

(4)(–2)(–2)(–2)(–2) Use PEMDAS.

(–8)(–2)(–2)(–2)

(16)(–2)(–2)

(–32)(–2)

64

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24 – (8 – 1.2 5)2Substitute 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 ExponentsLESSON 2-6

Additional Examples

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Simplify 32 + 62 – 14 • 3.

32 + 62 – 14 • 3 = 32 + 36 – 14 • 3 Exponent: 62 = 6 • 6 = 36.

= 32 + 36 – 42 Multiply 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 ExponentsLESSON 2-6

Additional Examples

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Evaluate 5x + 32 ÷ p for x = 2 and p = 3.

5x + 32 ÷ p = 5 • 2 + 32 ÷ 3 Substitute 2 for x and 3 for p.

= 5 • 2 + 9 ÷ 3 Exponent (Power).

= 10 + 3 Multiply and Divide from left to right.

= 13 Add and Subtract from left to right.

Positive ExponentsLESSON 2-6

Additional Examples

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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 taxC = p + r • p

sales tax rate (in fraction or decimal form)C = p + r • p

= 32 + 0.08 • 32 Substitute 32 for p. Change 8% to 0.08 and substitute 0.08 for r.

= 32 + 2.56 Multiply first.

= 34.56 Then add.

The total cost of the jeans is $34.56.

Positive ExponentsLESSON 2-6

Additional Examples

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Write each expression using an exponent.

1. 6 • 6 2. 8 • 8 • 8

Simplify each expression.

3. 54 4. 3.22

5. 23 + (10 – 5) 6. 32 • (9 – 2) + 1

62 83

625 10.24

13 64

Positive ExponentsLESSON 2-6

Lesson Quiz