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Jenna Beckley EXPONENTS

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Click on the arrows buttons or answers when prompted in order to continue DIRECTIONS Button

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Student Teacher

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OBJECTIVES Given the module, students will be able to simplify, multiply, divide and find powers of expressions containing negative and fractional exponents with 100% accuracy.

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Algebra II Students 9 th -11 th Grade Students who have already learned about exponentsthis is a cumulative review of the properties TARGET AUDIENCE

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Students will be a in a computer lab or with personal computers in a classroom using the PowerPoint Materials Computers with internet access PowerPoint Loose leaf Pencil LEARNING ENVIRONMENT

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Algebra 2 Standard 5 Rational and Radical Expressions, Equations, and Functions STANDARDS

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Population Growth Area and Volume Measurements Scientific Notation Interest Rates Simplifying Large Numbers Computer Programming WHEN ARE EXPONENTS USED IN REAL LIFE?

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Method 1.Check for similar bases 2.Add the exponents 3.Simplify if there are any negative exponents x2x7x2x7 1.x is the base 2.x 2+7 =x 9 MULTIPLYING EXPRESSIONS WITH EXPONENTS

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The same rules apply when there are negative or fractional exponents involved 2 5 2 -7 1.2 is the base 2.2 5+(-2) =2 3 MULTIPLYING EXPRESSIONS WITH EXPONENTS CONTINUED

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5 4 5 5 A.A.5 20 B.B.5 9 C.C.5 D.D.5 8 YOUR TURN!

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5 4 5 5 =5 9 1.5 is the base 2.5 4+5 =5 9 CORRECT!

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5 4 5 5 =5 9 1.5 is the base 2.5 4+5 =5 9 INCORRECT

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Method 1.Check for the same base 2.Subtract the exponent in the denominator from the exponent in the numerator 3.Simplify if there are any negative exponents DIVIDING EXPRESSIONS WITH EXPONENTS

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The same rules apply when there are negative or fractional exponents DIVIDING EXPRESSIONS WITH EXPONENTS CONTINUED

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7 6 7 4 A.A. 1_ 7 2 B.B.7 2 C.C.7 10 D.D.7 3/2 YOUR TURN!

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CORRECT!

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INCORRECT

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Method 1.Multiply the exponents 2.Simplify if there are any negative exponents (x 6 ) 7 1.x 67 =x 42 RAISING AN EXPONENTIAL EXPRESSION TO AN EXPONENT

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The same rules apply when using negative or fractional exponents RAISING AN EXPONENTIAL EXPRESSION TO AN EXPONENT

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YOUR TURN!

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CORRECT!

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INCORRECT

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EXPRESSIONS WITH MULTIPLE BASES

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Method 1.Match up bases 2.Use rules for multiplying, dividing, and raising to an exponent for exponential expressions 3.Simplify if there are any negative exponents 4 4 5 -3 5 6 5 2 4 2 1.4 45 -3 5 6 4 25 2 2.=4 4-25 -3+6-2 =4 25 EXPRESSIONS WITH MULTIPLE BASES

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Method 1.Match up bases 2.Use rules for multiplying, dividing, and raising to an exponent for exponential expressions 3.Simplify if there are any negative exponents a 6 b 7 c -1/2 a -2 a 10 b 4 c 3/2 1.a 6 a 2b 7c -1/2 a 10 b 4 c 3/2 2.=a 6+2-10b 7-4c -1/2-3/2 =a -2b 3c -2 3.= b 3 a 2 c 2 EXAMPLE

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6 3 5 4 6 -2 5 7 6 -1 A.A.6 2 5 11 B.B.5 11 6 C.C.6 3 5 3 D.D.6 2 5 3 YOUR TURN!

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6 3 5 4 6 -2 5 7 6 -1 1.6 3 6 -25 4 6 -1 5 7 2.=6 3+(-2)-(-1)5 4-7 =6 25 -3 3.= 6 2 5 3 CORRECT!

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INCORRECT 6 3 5 4 6 -2 5 7 6 -1 1.6 3 6 -25 4 6 -1 5 7 2.=6 3+(-2)-(-1)5 4-7 =6 25 -3 3.= 6 2 5 3

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Youve been using negative and fractional exponents, but do you know what negative and fractional exponents are? Fractional Exponents Negative Exponents Or if you already know about fractional and negative exponents, you can take the quiz. Quiz

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Explanation x a/b The numerator, a, is what the base, x, is raised to The denominator, b, is the b th root of the base, x x3/2x3/2 3 is the power x is raised to 2 is asking for the 2 nd root of x So x 3/2 is the second root of x 3 FRACTIONAL EXPONENTS

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You can choose which one you do first raise the base to the numerator take the root determined by the denominator Remember to do both steps FRACTIONAL EXPONENTS CONTINUED

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Raising the Base to the Numerator First Taking the Root Determined by the Denominator First 4 3/2 =2 3 =8 *Note that the answer from both methods is the same EXAMPLE

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Raising the Base to the Numerator First Taking the Root Determined by the Denominator First 27 2/3 =3 2 =9 EXAMPLE Quiz Negative Exponents

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A positive exponent tells you how many times to multiply the base A negative exponent tells you how many times to divide the base NEGATIVE EXPONENTS

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Positive ExponentNegative Exponent EXAMPLE

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reciprocal reciprocal So basically, with negative exponents, take the reciprocal of the base and then use the absolute value of the exponent. The reciprocal of a number is 1 over that number.

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EXAMPLE

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Quiz Fractional Exponents

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Quiz No calculators Simplify the expression on your loose leaf paper Select the answer on the screen If you get a problem wrong, you will be taken back to that part of the lesson, and then you will be able to return to the quiz

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A.A.3 21 B.B.3 14 C. C. 3 48 D.D.3 20 1. (3 3 3 5 ) 6

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Correct! C. 3 48 is the correct answer

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Incorrect

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Method 1.Check for similar bases 2.Add the exponents 3.Simplify if there are any negative exponents x2x7x2x7 1.x is the base 2.x 2+7 =x 9 MULTIPLYING EXPRESSIONS WITH EXPONENTS

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Method 1.Multiply the exponents 2.Simplify if there are any negative exponents (x 6 ) 7 1.x 67 =x 42 RAISING AN EXPONENTIAL EXPRESSION TO AN EXPONENT

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A.A.a 10 B.B.a 4 C.C.a 21 D.D.a 7/3 2. a 7 a 3

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Correct! B. a 4 is the correct answer

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Incorrect

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Method 1.Check for the same base 2.Subtract the exponent in the denominator from the exponent in the numerator 3.Simplify if there are any negative exponents DIVIDING EXPRESSIONS WITH EXPONENTS

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Correct!

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Incorrect

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Method 1.Check for the same base 2.Subtract the exponent in the denominator from the exponent in the numerator 3.Simplify if there are any negative exponents DIVIDING EXPRESSIONS WITH EXPONENTS

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Method 1.Multiply the exponents 2.Simplify if there are any negative exponents (x 6 ) 7 1.x 67 =x 42 RAISING AN EXPONENTIAL EXPRESSION TO AN EXPONENT

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4. 8 -3 7 8 8 4 7 9/2 8 -2

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Correct!

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Incorrect

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Method 1.Check for similar bases 2.Add the exponents 3.Simplify if there are any negative exponents x2x7x2x7 1.x is the base 2.x 2+7 =x 9 MULTIPLYING EXPRESSIONS WITH EXPONENTS

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Method 1.Check for the same base 2.Subtract the exponent in the denominator from the exponent in the numerator 3.Simplify if there are any negative exponents DIVIDING EXPRESSIONS WITH EXPONENTS

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Method 1.Match up bases 2.Use rules for multiplying, dividing, and raising to an exponent for exponential expressions 3.Simplify if there are any negative exponents 4 4 5 -3 5 6 5 2 4 2 1.4 45 -3 5 6 4 25 2 2.=4 4-25 -3+6-2 =4 25 EXPRESSIONS WITH MULTIPLE BASES

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A.A. 5 5 B.B. 5 9 C.C. 5 14 D.D. 5 2/7 5. 5 2 5 7

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Correct! B. 5 9 is the correct answer

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Incorrect

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Method 1.Check for similar bases 2.Add the exponents 3.Simplify if there are any negative exponents x2x7x2x7 1.x is the base 2.x 2+7 =x 9 MULTIPLYING EXPRESSIONS WITH EXPONENTS

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Correct!

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Incorrect

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Method 1.Multiply the exponents 2.Simplify if there are any negative exponents (x 6 ) 7 1.x 67 =x 42 RAISING AN EXPONENTIAL EXPRESSION TO AN EXPONENT

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Correct!

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Incorrect

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Method 1.Check for similar bases 2.Add the exponents 3.Simplify if there are any negative exponents x2x7x2x7 1.x is the base 2.x 2+7 =x 9 MULTIPLYING EXPRESSIONS WITH EXPONENTS

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Method 1.Check for the same base 2.Subtract the exponent in the denominator from the exponent in the numerator 3.Simplify if there are any negative exponents DIVIDING EXPRESSIONS WITH EXPONENTS

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Method 1.Multiply the exponents 2.Simplify if there are any negative exponents (x 6 ) 7 1.x 67 =x 42 RAISING AN EXPONENTIAL EXPRESSION TO AN EXPONENT

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A.A.b 3 c 2 B.B.b 9 c 3 C.C.b 9 c 18 D.D.b 3 c 3 8. b 7/3 C 6 C -3 b 2/3

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Correct! D. b 3 c 3 is the correct answer

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Incorrect

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Method 1.Check for similar bases 2.Add the exponents 3.Simplify if there are any negative exponents x2x7x2x7 1.x is the base 2.x 2+7 =x 9 MULTIPLYING EXPRESSIONS WITH EXPONENTS

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Method 1.Match up bases 2.Use rules for multiplying, dividing, and raising to an exponent for exponential expressions 3.Simplify if there are any negative exponents 4 4 5 -3 5 6 5 2 4 2 1.4 45 -3 5 6 4 25 2 2.=4 4-25 -3+6-2 =4 25 EXPRESSIONS WITH MULTIPLE BASES

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A.A. x 4 B.B. x 3 C.C. x 1/3 D. D. x 8 9. x 6 x 2

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Correct! A. x 4 is the correct answer

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Incorrect

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Method 1.Check for the same base 2.Subtract the exponent in the denominator from the exponent in the numerator 3.Simplify if there are any negative exponents DIVIDING EXPRESSIONS WITH EXPONENTS

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Correct!

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Incorrect

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Method 1.Check for the same base 2.Subtract the exponent in the denominator from the exponent in the numerator 3.Simplify if there are any negative exponents DIVIDING EXPRESSIONS WITH EXPONENTS

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Method 1.Multiply the exponents 2.Simplify if there are any negative exponents (x 6 ) 7 1.x 67 =x 42 RAISING AN EXPONENTIAL EXPRESSION TO AN EXPONENT

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Congratulations! Youve completed the lesson! Finish