The exponent of a number shows you how many times the number is being multiplied by itself.
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1 Name Evaluating Numerical Expressions with Exponents- Step-by-Step Lesson Lesson 1 Exponent Problem: Write the expression as an exponent. 4 x 4 x 4 x 4 x 4 Explanation: The exponent of a number shows you how many times the number is being multiplied by itself. The number of times it is multiplied by itself is written as a small number to the right and above the base number. This number (4) is being multiplied by itself 5 times, so it will be written as: 4 5 In this: 4 5 = 4 4 x 4 x 4 x 4 = 1024 Other names for an exponent are an index or a power.
2 Name Evaluating Numerical Expressions with Exponents- Guided Lesson Complete the following problems: 1) Evaluate. 6 5 = 2) Evaluate = 3) Evaluate =
3 Name Evaluating Numerical Expressions with Exponents- Guided Lesson Explanation Explanation#1 The exponent of a number tells you how many times it should be multiplied by itself. In 6 5 the "5" says to multiply 6 by itself 5 times, so 6 5 = 6 6 x 6 x 6 x 6 = 7776 So, the answer is Explanation#2 The exponent of a number tells you how many times it should be multiplied by itself. In 7 4 the "4" says to multiply 7 by itself 4 times, so 7 4 = 7 7 x 7 x 7 = 2,401 In 9 6 the "6" says to multiply 9 by itself 6 times, so 9 6 = 9 9 x 9 x 9 x 9 x 9 = 531,441 Step 3) Now we can add this number. 2, ,441 = 533,842 So, the answer is 533,842. Explanation#3 Using the same concept we find the value of each number and then calculate the difference. In 8 4 the "4" says to multiply 8 by itself 4 times, so 8 4 = 8 8 x 8 x 8 = 4096 In 3 7 the "7" says to multiply 3 by itself 7 times, so 3 7 = 3 3 x 3 x 3 x 3 x 3 x 3 = 2187 Step 3) Now we can subtract this number = 1909 So, the answer is 1909.
4 Name Evaluating Numerical Expressions with Exponents- Independent Practice Complete all the problems. 1. Evaluate. 2 8 = 2. Write the expression as an exponent. 7 x 7 x 7 x 7 x 7 x 7 x 7 3. Evaluate = 4. Evaluate = 5. Write the expression as an exponent. 5 x 5 x 5 x 5
5 Name 6. Write the expression as an exponent. 9 x 9 x 9 x 9 x 9 7. Evaluate = 8. Evaluate. 3 8 = 9. Evaluate = 10. Write the expression as an exponent. 8 x 8 x 8 x 8 x 8 x 8 x 8
6 Name Evaluating Numerical Expressions with Exponents- Matching Worksheet Match the problems to their answers. Write the letter of the answer that matches the problem. 1. Evaluate = a Write the expression as an exponent. 11 x 11 x 11 b Evaluate = c Evaluate = d Write the expression as an exponent. 14 x 14 x 14 x 14 x 14 e Evaluate = f Evaluate = g Evaluate. 8 8 = h Write the expression as an exponent. 10 x 10 x 10 x 10 x 10 x Evaluate = i j. 11
7 Topic: Writing Exponents - Worksheet 1 Write in exponential form X 8 = 2. 2 X 2 X 2 X 2 = = = 5. 7 X 7 X 5 X 5 = 6. 4 X 4 X 4 X 4 = 7. ( -8 ) X ( -8 ) X ( -8 ) = 8. ( -6 ) X ( -6 ) X ( -2 ) X ( -2 ) X ( -2 ) = 9. ( 1/4 ) X ( 1/4 ) X ( 1/4 ) = =
8 Topic: Writing Exponents - Worksheet 2 Write in exponential form X 12 = 2. 4 X 4 X 4 X 4 = = = 5. 3 X 3 X 6 X 6 = X 11 X 8 X 8 X 8 = 7. ( -15 ) X ( -15 ) X ( -15 ) = 8. ( -7 ) X ( -7 ) X ( -4 ) X ( -4 ) X ( -4 ) = 9. ( 1/5 ) X ( 1/5 ) X ( 1/5 ) = =
9 Topic: Writing Exponents - Worksheet 3 Write in exponential form X 5 = 2. 7 X 7 X 7 X 7 = = = 5. 4 X 4 X 2 X 2 = 6. 3 X 3 X 5 X 5 X 5 = 7. ( -9 ) X ( -9 ) X ( -9 ) = 8. ( -8 ) X ( -8 ) X ( -5 ) X ( -5 ) X ( -5 ) = 9. ( 1/6 ) X ( 1/6 ) X ( 1/6 ) = =
10 Topic: Writing Exponents - Worksheet 4 Write in exponential form X 9 = 2. 6 X 6 X 6 X 6 = = = 5. 8 X 8 X 3 X 3 = 6. 2 X 2 X 6 X 6 X 6 = 7. ( -8 ) X ( -8 ) X ( -8 ) = 8. ( -9 ) X ( -9 ) X ( -3 ) X ( -3 ) X ( -3 ) = 9. ( 1/7 ) X ( 1/7 ) X ( 1/7 ) = =
11 Topic: Writing Exponents - Worksheet 5 Write in exponential form X 6 = 2. 5 X 5 X 5 X 5 = = = 5. 9 X 9 X 5 X 5 = 6. 4 X 4 X 9 X 9 X 9 = 7. ( -7 ) X ( -7 ) X ( -7 ) = 8. ( -10 ) X ( -10 ) X ( -2 ) X ( -2 ) X ( -2 ) = 9. ( 1/9 ) X ( 1/9 ) X ( 1/9 ) = =
12 Topic : Multiplying and Dividing Exponents - Worksheet 1 Write your answers in expanded form = = X 9 2 = X2 2 X5 2 = = 6. 8/(8 3 ) = 7. ( 7 5 ) 2 = X 3 3 = 9. ( 6-2 ) 3 = =
13 Topic: Multiplying and Dividing Exponents - Worksheet 2 Write your answers in expanded form = = X 5 2 = X2 5 X2 2 = = 6. (4/3) 3 = 7. ( 6 4 ) 2 = X 5 2 = 9. ( 3-2 ) 2 = =
14 Topic : Multiplying and Dividing Exponents - Worksheet 3 Write your answers in expanded form = = X 5 2 = X5 5 X6 2 = = 6. (2/3) 3 = 7. ( 10 4 ) 3 = X 2 2 = 9. ( 3-2 ) -2 = =
15 Topic : Multiplying and Dividing Exponents - Worksheet 4 Write your answers in expanded form = = X 5 3 = X6 3 X4 2 = = 6. (2/5) 3 = 7. ( 7 5 ) 3 = X 6 2 = 9. ( 8-2 ) 3 = =
16 Topic : Multiplying and Dividing Exponents - Worksheet 5 Write your answers in expanded form = = X 6 2 = X5 6 X4 2 = = 6. (3/5) 7 = 7. ( 16 2 ) 4 = X 5 2 = 9. ( 7-3 ) 4 = =
17 Topic: Evaluate Expressions with Fractional Exponents - Worksheet 1 Evaluate the following: 1. (29) -1/2 2. (6000) 2/3 3. (72560) 2/4 4. (56) 7/2 5. D -3/2.D 1/2,when D=5 6. Evaluate -a-a 1/3, when a=20 7. C 3/2.c 1/2,when c=6 8. Evaluate -(1/m) -5/4, when m=8 9. Evaluate -a-a 1/2, when a= C 2/3.c 1/3,when c=50
18 Topic : Evaluate Expressions with Fractional Exponents - Worksheet 2 Evaluate the following: 1. (15) -1/2 2. (4000) 5/3 3. (65270) 2/3 4. (47) 6/2 5. K 3/2.K 1/2,when K=7 6. Evaluate -b-b 1/3, when b=15 7. A 3/2.A 1/2,when A=8 8. Evaluate -(1/n) -6/3, when n=6 9. Evaluate -a-a 3/2, when a= c 5/3.c 2/3,when c=40
19 Topic : Evaluate Expressions with Fractional Exponents - Worksheet 3 Evaluate the following: 1. (10) -1/2 2. (5000) 5/3 3. (55000) 2/3 4. (52) 6/2 5. J 3/2.J 1/2,when J=5 6. Evaluate -d-d 1/3, when d=16 7. A 3/2.A 1/2,when A=8 8. Evaluate -(1/n) -6/3, when n=6 9. Evaluate -e-e 3/2, when e= r 5/3.r 2/3,when r=55
20 Topic : Evaluate Expressions with Fractional Exponents - Worksheet 4 Evaluate the following: 1. (25) -1/2 2. (2500) 2/3 3. (70000) 2/3 4. (85) 3/2 5. y 1/2.y 1/2,when y=8 6. Evaluate -w-w 1/2, when w=20 7. F 2/2.f 1/2,when f=8 8. Evaluate -(1/t) -6/3, when t=12 9. Evaluate -q-q 3/2, when q=7 10. a 5/2.a 2/3,when a=30
21 Topic : Evaluate Expressions with Fractional Exponents - Worksheet 5 Evaluate the following: 1. (78) -1/2 2. (5520) 2/3 3. (8000) 2/3 4. (45) 3/2 5. h 1/2.h 1/2,when h=12 6. Evaluate -a-a 1/2, when a=45 7. X 3/2.x 1/2,when x=7 8. Evaluate -(1/v) -5/3, when v=15 9. Evaluate -t-t 3/2, when t= b 5/2.b 2/3,when b=25
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