Question

Based on what you've read, answer the following questions.

What number, when substituted for x in the following problem, will make the problem true?

6x + 8x = 10x


How can you insert two radical signs in the following problem to make it true?

5 = 4 + 4 + 4⁄4


Square the following numbers.

a. 4

b. 6

c. 13

d. 10


Cube the following numbers.

a. 1

b. 2

c. 4

d. 8


Rewrite the following exponential abbreviations as multiplication problems.

a. 22

b. 84

c. 123

d. 205


Write the following multiplications as exponential abbreviations.

a. 5 × 5

b. 7 × 7 × 7 × 7

c. 2 × 2 × 2

d. 9 × 9 × 9 × 9 × 9


Write the values of the following exponential abbreviations.

a. 33

b. 142

c. 125

d. 90

e. 44

f. 171


Rewrite each number using scientific notation.

a. 7,600

b. 23,400

c. 167,000

d. 2,000,000,000


Rewrite each scientific notation as a regular number.

a. 9.7 × 104

b. 7 × 105

c. 8.97 × 107

d. 3.2 × 1010


Find each of the following square roots. (Hint: All examples are perfect squares.)

a. √16

b. √169

c. √64

d. √400


ANSWER:
1.If you substitute the number 2 for x in the problem, you’ll make it true.

a.6x + 8x = 10x

b.62 + 82 = 102

c.36 + 64 = 100

d. 100 = 100

2. Insert two radical signs into the problem like this to make it true:

5 = 5 √4 + √4 + 4⁄4

5 = 2 + 2 + 1

5 = 5

3. a. 42 = 4 × 4 = 16

b. 62 = 6 × 6 = 36

c. 132 = 13 × 13 = 169

d. 102 = 10 × 10 = 100

4. a. 13 = 1 × 1 × 1 = 1

b. 23 = 2 × 2 × 2 = 8

c. 43 = 4 × 4 × 4 = 64

d. 83 = 8 × 8 × 8 = 512

5. a. 2 × 2

b. 8 × 8 × 8 × 8

c. 12 × 12 × 12

d. 20 × 20 × 20 × 20 × 20

6. a. 52

b. 74

c. 23

d. 95

7. a. 33 = 3 × 3 × 3 = 27

b. 142 = 14 × 14 = 196

c. 125 = 12 × 12 × 12 × 12 × 12 = 248,832

d. 90 = 1 (Any number to the zero power equals 1.)

e. 44 = 4 × 4 × 4 × 4 = 256

f. 171 = 17 (Any number to the first power equals itself.)

8. a. 7.6 × 103

(103 = 1,000 and 7.6 × 1,000 = 7,600)

b. 2.34 × 104

(104 = 10,000 and 2.34 × 10,000 = 23,400)

c. 1.67 × 105

(105 = 100,000 and 1.67 × 100,000 = 167,000)

d. 2 × 109

(109 = 1,000,000,000 and 2 × 1,000,000,000 = 2,000,000,000)

9. a. 97,000

(9.7 × 10 × 10 × 10 × 10 = 97,000)

b. 700,000

(7 × 10 × 10 × 10 × 10 × 10 = 700,000)

c. 89,700,000

(8.97 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 89,700,000)

d. 32,000,000,000

(3.2 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 32,000,000,000)

10. a. 4 (4 × 4 = 16)

b. 13 (13 × 13 = 169)

c. 8 (8 × 8 = 64)

d. 20 (20 × 20 = 400)

Answer 1

1. If you substitute the number 2 for x in the problem, you’ll make it true.

6x + 8x = 10x

62 + 82 = 102

36 + 64 = 100

100 = 100

2. Insert two radical signs into the problem like this to make it true:

5 = 5 √4 + √4 + 4⁄4

5 = 2 + 2 + 1

5 = 5

3. a. 42 = 4 × 4 = 16

b. 62 = 6 × 6 = 36

c. 132 = 13 × 13 = 169

d. 102 = 10 × 10 = 100

4. a. 13 = 1 × 1 × 1 = 1

b. 23 = 2 × 2 × 2 = 8

c. 43 = 4 × 4 × 4 = 64

d. 83 = 8 × 8 × 8 = 512

5. a. 2 × 2

b. 8 × 8 × 8 × 8

c. 12 × 12 × 12

d. 20 × 20 × 20 × 20 × 20

6. a. 52

b. 74

c. 23

d. 95

7. a. 33 = 3 × 3 × 3 = 27

b. 142 = 14 × 14 = 196

c. 125 = 12 × 12 × 12 × 12 × 12 = 248,832

d. 90 = 1 (Any number to the zero power equals 1.)

e. 44 = 4 × 4 × 4 × 4 = 256

f. 171 = 17 (Any number to the first power equals itself.)

8. a. 7.6 × 103

(103 = 1,000 and 7.6 × 1,000 = 7,600)

b. 2.34 × 104

(104 = 10,000 and 2.34 × 10,000 = 23,400)

c. 1.67 × 105

(105 = 100,000 and 1.67 × 100,000 = 167,000)

d. 2 × 109

(109 = 1,000,000,000 and 2 × 1,000,000,000 = 2,000,000,000)

9. a. 97,000

(9.7 × 10 × 10 × 10 × 10 = 97,000)

b. 700,000

(7 × 10 × 10 × 10 × 10 × 10 = 700,000)

c. 89,700,000

(8.97 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 89,700,000)

d. 32,000,000,000

(3.2 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 32,000,000,000)

10. a. 4 (4 × 4 = 16)

b. 13 (13 × 13 = 169)

c. 8 (8 × 8 = 64)

d. 20 (20 × 20 = 400)

Explanation:

Answer 2

If you substitute the number 2 for x in the problem, you’ll make it true.

6x + 8x = 10x

62 + 82 = 102

36 + 64 = 100

100 = 100

Insert two radical signs into the problem like this to make it true:

5 = 5 √4 + √4 + 4⁄4

5 = 2 + 2 + 1

5 = 5

a. 42 = 4 × 4 = 16

b. 62 = 6 × 6 = 36

c. 132 = 13 × 13 = 169

d. 102 = 10 × 10 = 100

a. 13 = 1 × 1 × 1 = 1

b. 23 = 2 × 2 × 2 = 8

c. 43 = 4 × 4 × 4 = 64

d. 83 = 8 × 8 × 8 = 512

a. 2 × 2

b. 8 × 8 × 8 × 8

c. 12 × 12 × 12

d. 20 × 20 × 20 × 20 × 20

a. 52

b. 74

c. 23

d. 95

a. 33 = 3 × 3 × 3 = 27

b. 142 = 14 × 14 = 196

c. 125 = 12 × 12 × 12 × 12 × 12 = 248,832

d. 90 = 1 (Any number to the zero power equals 1.)

e. 44 = 4 × 4 × 4 × 4 = 256

f. 171 = 17 (Any number to the first power equals itself.)

a. 7.6 × 103

(103 = 1,000 and 7.6 × 1,000 = 7,600)

b. 2.34 × 104

(104 = 10,000 and 2.34 × 10,000 = 23,400)

c. 1.67 × 105

(105 = 100,000 and 1.67 × 100,000 = 167,000)

d. 2 × 109

(109 = 1,000,000,000 and 2 × 1,000,000,000 = 2,000,000,000)

a. 97,000

(9.7 × 10 × 10 × 10 × 10 = 97,000)

b. 700,000

(7 × 10 × 10 × 10 × 10 × 10 = 700,000)

c. 89,700,000

(8.97 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 89,700,000)

d. 32,000,000,000

(3.2 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 32,000,000,000)

a. 4 (4 × 4 = 16)

b. 13 (13 × 13 = 169)

c. 8 (8 × 8 = 64)

d. 20 (20 × 20 = 400)

Explanation:

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