Question

Which expression is correctly developed to use the Product Rule of Exponents?


62⋅73
6 squared times 7 cubed

108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline

327
32 superscript 7 baseline

(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline

Answer 1

Which of the following correctly used the Product Rule of Exponents to simplify the expression 100^8⋅100^7?(1 point)
Responses

200^15
200 superscript 15 baseline

100^15
100 superscript 15 baseline

100^56
100 superscript 56 baseline

10,000^15

Answer 2

Product Rule of Exponents Quick Check
3 of 53 of 5 Items
Question
Find the numerical equivalent of 102 ⋅103(1 point)
Responses

100,000
100,000

1,100
1,100

10
10

105

Answer 3

Find the numerical equivalent of 25 ⋅2−2(1 point)
Responses

8
8

128
128

2
2

16

Answer 4

Find the numerical equivalent of 2^5 ⋅2^−2(1 point)
Responses

8
8

128
128

2
2

16

Answer 5

Question
Find the numerical equivalent of 4^9⋅4^−7(1 point)
Responses

16
16

416
4 superscript 16 baseline

4
4

42

Answer 6

(52)9

Answer 7

100^8⋅100^7 simplifies to 100^(8+7) using the Product Rule of Exponents, which is equal to 100^15. Therefore, the correct option is 100^15.

Answer 8

102 ⋅103 simplifies to 10^(2+3) using the Product Rule of Exponents, which is equal to 10^5. Therefore, the correct response is 100,000.

Answer 9

25 ⋅2^(-2) simplifies to 25 * (1/2^2) using the Product Rule of Exponents. 2^(-2) is equal to 1/2^2 or 1/4. Therefore, the expression simplifies to 25 * (1/4) which is equal to 25/4 or 6.25. None of the given responses (8, 128, 2, 16) matches the correct answer.

Answer 10

2^5 ⋅2^(-2) simplifies to 2^(5+(-2)) using the Product Rule of Exponents. 5+(-2) is equal to 3. Therefore, the expression simplifies to 2^3 which is equal to 8. The correct response is 8.

Answer 11

4^9⋅4^(-7) simplifies to 4^(9+(-7)) using the Product Rule of Exponents. 9+(-7) is equal to 2. Therefore, the expression simplifies to 4^2 which is equal to 16. The correct response is 16.