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Ch 1 Sec 8: Slide #1 Columbus State Community College Chapter 1 Section 8 Exponents and Order of Operations

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Ch 1 Sec 8: Slide #2 Exponents and Order of Operations 1.Use exponents to write repeated factors. 2.Simplify expressions containing exponents. 3.Use the order of operations. 4.Simplify expressions with fraction bars.

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Ch 1 Sec 8: Slide #3 Exponents An exponent is a quick way to write repeated multiplication. For example, Base 3 3 3 3 can be written 3 4 Exponent This is called exponential notation or exponential form. To simplify 3 4, actually do the multiplication. 3 4 = 3 3 3 3 = 81

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Ch 1 Sec 8: Slide #4 Reading Common Exponents Here are some examples of how to read common exponents. 3 1 is read 3 to the first power. 3 2 is read 3 to the second power or, more commonly, 3 squared. 3 3 is read 3 to the third power or, more commonly, 3 cubed. 3 4 is read 3 to the fourth power. 3 5 is read 3 to the fifth power.

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Ch 1 Sec 8: Slide #5 Using Exponents EXAMPLE 1 Using Exponents Rewrite each multiplication using exponents. Also indicate how to read the exponential form. (a) 10 10 10 can be written as 10 6, which is read 10 to the sixth power. (b) ( 7 )( 7 )can be written as 7 2, which is read 7 squared or 7 to the second power. (c) 2can be written as 2 1, which is read 2 to the first power.

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Ch 1 Sec 8: Slide #6 Using Exponents with Negative Numbers EXAMPLE 2 Using Exponents with Negative Numbers Simplify. (a) ( – 2 ) 3 = ( – 2 ) ( – 2 ) ( – 2 ) 4 ( – 2 ) –8–8 (b) ( – 2 ) 4 = ( – 2 ) ( – 2 ) ( – 2 ) ( – 2 ) – 8 ( – 2 )From 2(a), ( – 2 ) 3 = – 8. 16

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Ch 1 Sec 8: Slide #7 Using Exponents with Negative Numbers EXAMPLE 2 Using Exponents with Negative Numbers Simplify. (c) ( – 5 ) 2 ( – 2 ) 3 ( 25 ) ( – 8 ) – 200 = ( – 5 ) ( – 5 ) ( – 2 ) ( – 2 ) ( – 2 ) ( – 5 ) 2 ( – 2 ) 3

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Ch 1 Sec 8: Slide #8 ^ Calculator Tip – TI-30X IIS Calculator Tip On your TI-30X IIS calculator, use the exponent key to enter exponents. To enter 7 5, press the following keys. ^ 7 ^ 5= 16807

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Ch 1 Sec 8: Slide #9 Calculator Tip On your TI-30Xa calculator, use the exponent key to enter exponents. To enter 7 5, press the following keys. yxyx yxyx Calculator Tip – TI-30Xa 7 yxyx 5= 16807

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Ch 1 Sec 8: Slide #10 Working from Left to Right EXAMPLE 3 Working from Left to Right Simplify. (a) – 3 – – 8 + – 2Do additions and subtractions from left to right. 5 + – 2 3

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Ch 1 Sec 8: Slide #11 Working from Left to Right EXAMPLE 3 Working from Left to Right Simplify. (b) – 20 ÷ 2 5Do multiplications and divisions from left to right. – 10 5 – 50

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Ch 1 Sec 8: Slide #12 Mixing Operations 10 + 2 3 12 3 36 10 + 2 3 10 + 6 16 Compare the methods used to simplify the following example. If we work from left to rightIf we multiply first 10 + 2 3 Mathematicians have agreed to do things in a certain order. In this example, we multiply before we add.

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Ch 1 Sec 8: Slide #13 Order of Operations Step 1Work inside parentheses or other grouping symbols. Step 2Simplify expressions with exponents. Step 3Do the remaining multiplications and divisions as they occur from left to right. Step 4Do the remaining additions and subtractions as they occur from left to right.

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Ch 1 Sec 8: Slide #14 CAUTION To help in remembering the order of operations, you may have memorized the letters PEMDAS, or the phrase Please Excuse My Dear Aunt Sally. Please Excuse My Dear Aunt Sally 1. Parentheses 2. Exponents 3. Multiply & Divide (from left to right) 4. Add & Subtract (from left to right) Be careful! Do not automatically do all multiplication before division. Multiplication and division are done from left to right. Likewise, addition and subtraction are done from left to right.

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Ch 1 Sec 8: Slide #15 Calculator Tip Calculator Tip Enter the previous example in your calculator. 103=16+ x 2 If you have a scientific calculator, it automatically uses the order of operations and multiplies first to get the correct answer of 16.

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Ch 1 Sec 8: Slide #16 Using the Order of Operations with Whole Numbers EXAMPLE 4 Using the Order of Operations with Whole #s Simplify. 5 + 2 ( 24 – 4 2 ) ÷ 8Multiply inside parentheses first. 5 + 2 ( 24 – 8 ) ÷ 8 Subtract inside parentheses. 5 + 2 ( 16 ) ÷ 8 5 + 32 ÷ 8 5 + 4 9 Multiply. Divide. Add.

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Ch 1 Sec 8: Slide #17 Using the Order of Operations with Integers EXAMPLE 5 Using the Order of Operations with Integers Simplify. – 40 ÷ ( 12 – 7 ) – 4Subtract inside parentheses first. – 40 ÷ 5 – 4 Divide. – 8 – 4 – 12 Subtract. (a)

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Ch 1 Sec 8: Slide #18 Using the Order of Operations with Integers EXAMPLE 5 Using the Order of Operations with Integers Simplify. (b)6 + 5 ( 1 – – 3 ) ( 18 ÷ – 9 )Subtract inside parentheses first. 6 + 5 ( 4 ) ( 18 ÷ – 9 ) Divide inside parentheses. 6 + 5 ( 4 ) ( – 2 ) 6 + 20 ( – 2 ) 6 + – 40 – 34 Multiply from left to right. Multiply. Add.

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Ch 1 Sec 8: Slide #19 Using the Order of Operations with Exponents EXAMPLE 6 Using the Order of Operations with Exponents Simplify. ( – 5 ) 2 – ( – 2 ) 3 Apply exponents. 25 – – 8 Add. 33 (a)

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Ch 1 Sec 8: Slide #20 Using the Order of Operations with Exponents EXAMPLE 6 Using the Order of Operations with Exponents Simplify. (b)( – 3 ) 3 – ( 8 – 6 ) 3 ( 3 ) 2 Subtract inside parentheses first. ( – 3 ) 3 – ( 2 ) 3 ( 3 ) 2 Apply exponents. – 27 – 8 ( 9 ) – 27 – 72 – 99 Multiply. Add.

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Ch 1 Sec 8: Slide #21 Using the Order of Operations with Fraction Bars EXAMPLE 7 Using the Order of Operations with Fraction Bars Simplify. First, do the work in the numerator – 4 – 2 ( 3 – – 1 ) 2 3 – 4 ÷ 2 – 3 – 4 – 2 ( 4 ) 2 – 4 – 2 ( 16 ) – 4 – 32 – 36 Next, do the work in the denominator 3 – 4 ÷ 2 – 3 – 12 ÷ 2 – 3 – 6 – 3 18 – 36 18 = = –2–2

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Ch 1 Sec 8: Slide #22 Exponents and Order of Operations Chapter 1 Section 8 – End Written by John T. Wallace

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