Slide 1 : Warm Up Lesson Presentation Lesson Quiz
Slide 2 : Warm Up
Simplify.
1. 2(2)
2. (–2)(–2)
3. (–2)(–2)(–2)
4. 3(3)(3) 4 4 –8 27 5.
Slide 3 : Evaluate expressions containing exponents. Objective
Slide 4 : power
base
exponent Vocabulary
Slide 5 : A power is an expression written with an exponent and a base or the value of such an expression. 3² is an example of a power. The base is the
number that is
used as a factor. The exponent, 2 tells
how many times the
base, 3, is used as a
factor.
Slide 6 : When a number is raised to the second power, we usually say it is “squared.” The area of a square is s ? s = s2, is the side length.
Slide 7 : Write the power represented by the geometric model. The figure is 5 units long, 5 units wide, and 5 units tall. 5 ? 5 ? 5 The factor 5 is used 3 times. 53 Example 1A: Writing Powers for Geometric Models
Slide 8 : Write the power represented by the geometric model. The figure is 6 units long and 6 units wide. 6 x 6 The factor 6 is used 2 times. 62 6 6 Example 1B: Writing Powers for Geometric Models
Slide 9 : Write the power represented by each geometric model. a. 22 b. Check It Out! Example 1 The figure is 2 units long and 2 units wide. 2 ? 2 The factor 2 is used 2 times. The figure is x units long, x units wide, and x units tall. x ? x ? x The factor x is used 3 times. x3
Slide 10 : There are no easy geometric models for numbers raised to exponents greater than 3, but you can still write them using repeated multiplication or a base and exponent. 3 to the second power, or 3 squared 3 ? 3 ? 3 ? 3 ? 3 Multiplication Power Value Words 3 ? 3 ? 3 ? 3 3 ? 3 ? 3 3 ? 3 3 3 to the first power 3 to the third power, or 3 cubed 3 to the fourth power 3 to the fifth power 3 9 27 81 243 31 Reading Exponents 32 33 34 35
Slide 11 :
Slide 12 : Evaluate each expression. A. (–6)3 (–6)(–6)(–6) –216 B. –102 –1 • 10 • 10 –100 Use –6 as a factor 3 times. Find the product of –1 and
two 10’s. Example 2: Evaluating Powers Think of a negative sign in front of a power as multiplying by a –1.
Slide 13 : Evaluate the expression.
C. Example 2: Evaluating Powers
Slide 14 : Evaluate each expression. a. (–5)3 b. –62 Check It Out! Example 2 (–5)(–5)(–5) Use –5 as a factor 3 times. –125 –1 ? 6 ? 6 –36 Think of a negative sign in front of a power as multiplying by –1. Find the product of –1 and
two 6’s.
Slide 15 : Check It Out! Example 2 Evaluate the expression.
c.
Slide 16 : Write each number as a power of the given base. A. 64; base 8 8 ? 8 82 B. 81; base –3 (–3)(–3)(–3)(–3) (–3)4 The product of two 8’s is 64. The product of four –3’s is 81. Example 3: Writing Powers
Slide 17 : Write each number as a power of a given base. a. 64; base 4 b. –27; base –3 Check It Out! Example 3 4 ? 4 ? 4 The product of three 4’s is 64. 43 (–3)(–3)(–3) –33 The product of three (–3)’s is –27.
Slide 18 : In case of a school closing, the PTA
president calls 3 families. Each of
these families calls 3 other families
and so on. How many families will have
been called in the 4th round of calls? The answer will be the number of families
contacted in the 4th round of calls. Example 4: Problem-Solving Application List the important information:
• The PTA president calls 3 families.
• Each family then calls 3 more families.
Slide 19 : Draw a diagram to show the number of
Families called in each round of calls. Example 4 Continued 2nd round of calls 1st round of calls PTA President
Slide 20 : Notice that after each round of calls the
number of families contacted is a power of 3. 1st round of calls: 1 ? 3 = 3 or 31 families contacted So, in the 4th round of calls, 34 families will have
been contacted. 34 = 3 ? 3 ? 3 ? 3 = 81 Multiply four 3’s. In the fourth round of calls, 81 families
will have been contacted. 2nd round of calls: 3 ? 3 = 9 or 32 families contacted 3rd round of calls: 9 ? 3 = 27 or 33 families contacted Example 4 Continued
Slide 21 : Drawing a diagram helps you visualize the
problem, but the numbers become too
large for a diagram. The diagram helps you
recognize the pattern of multiplying by 3
so that you can write the number as a
power of 3. Example 4 Continued
Slide 22 : What if…? How many bacteria will be on the slide after 8 hours? Check it Out! Example 4 28 After each hour, the number of bacteria is a power of 2. 2 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2 ? 2 Multiply eight 2’s. The product of eight 2’s. 256
Slide 23 : 1. Write the power represented by the geometric model. n n n2 Simplify each expression. 2. 4. 6? 3. –63 5. (–2)6 -216 216 64 Lesson Quiz Write each number as a power of the given base. 6. 343; base 7 7. 10,000; base 10 73 104