Question

Use the Product Rule of Exponents to simplify the expression 75 ⋅72.(1 point)

Answer 1

Find the numerical equivalent of 72⋅73(1 point)

Answer 2

wrong

Answer 3

Find the numerical equivalent of 7^2⋅7^3(1 point)

Answer 4

Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses

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

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

62⋅73
6 squared times 7 cubed

327

Answer 5

Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses

(5^2)9
left parenthesis 5 squared right parenthesis superscript 9 baseline

10^8⋅10^8
10 superscript 8 baseline times 10 superscript 8 baseline

6^2⋅7^3
6 squared times 7 cubed

32^7

Answer 6

Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses

20015
200 superscript 15 baseline

10056
100 superscript 56 baseline

10015
100 superscript 15 baseline

10,00015
10,000 superscript 15 baseline

Answer 7

Find the numerical equivalent of 102 ⋅103(1 point)
Responses

100,000
100,000

10
10

1,100
1,100

105

Answer 8

Find the numerical equivalent of 102 ⋅103(1 point)
Responses

100,000
100,000

10
10

1,100
1,100

10^5

Answer 9

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

128
128

2
2

16
16

8

Answer 10

5 of 55 of 5 Items
Question
Find the numerical equivalent of 49⋅4−7(1 point)
Responses

16
16

416
4 superscript 16 baseline

42
4 squared

4

Answer 11

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

16
16

416
4 superscript 16 baseline

42
4 squared

4

Answer 12

The Product Rule of Exponents states that when multiplying two exponents with the same base, you add the exponents.

In this case, we have 75 and 72, which both have a base of 7.

So, when we multiply 75 and 72, we add the exponents:

75 ⋅ 72 = 7^5 ⋅ 7^2 = 7^(5+2) = 7^7

Therefore, 75 ⋅ 72 simplifies to 7^7.

Answer 13

To find the numerical equivalent of 72⋅73, we simply perform the multiplication:

72⋅73 = 5256

Therefore, the numerical equivalent of 72⋅73 is 5256.

Answer 14

I apologize for the incorrect response. Let's calculate the correct numerical equivalent of 72⋅73.

72⋅73 = 5256

Therefore, the numerical equivalent of 72⋅73 is indeed 5256.

Answer 15

To find the numerical equivalent of 7^2 ⋅ 7^3, we can apply the rule of exponents, which states that when multiplying two exponents with the same base, we add the exponents.

Therefore, 7^2 ⋅ 7^3 can be simplified as 7^(2+3), which is equal to 7^5.

Using the definition of exponentiation, we know that 7^5 equals 7 * 7 * 7 * 7 * 7 = 16807.

Hence, the numerical equivalent of 7^2 ⋅ 7^3 is 16807.

Answer 16

The correct expression that can be developed to use the Product Rule of Exponents is: 62⋅73 (6 squared times 7 cubed).

Answer 17

The correct expression that can be developed to use the Product Rule of Exponents is: 6^2⋅7^3 (6 squared times 7 cubed).

Answer 18

To simplify the expression 1008 ⋅ 1007 using the Product Rule of Exponents, we add the exponents because the bases are the same.

1008 ⋅ 1007 = 10^3 ⋅ 10^2 = 10^(3+2) = 10^5

Therefore, the correct answer is 10015 (100 superscript 15 baseline).

Answer 19

To find the numerical equivalent of 102 ⋅ 103, we perform the multiplication.

102 ⋅ 103 = 1000

Therefore, the correct response is 1000.

Answer 20

To find the numerical equivalent of 102 ⋅103, we perform the multiplication.

102 ⋅ 103 = 1000

Therefore, the correct response is 1000.

Answer 21

To find the numerical equivalent of 2^5 ⋅2^−2, we can apply the rule of exponents, which states that when multiplying two exponents with the same base, we add the exponents.

Therefore, 2^5 ⋅ 2^−2 can be simplified as 2^(5-2), which is equal to 2^3, which simplifies further to 8.

Hence, the numerical equivalent of 2^5 ⋅2^−2 is 8.

Answer 22

To find the numerical equivalent of 49⋅4^(-7), we can use the rule of exponents which states that when the exponent is negative, we take the reciprocal of the base to that positive exponent.

We start by evaluating 4^(-7):

4^(-7) = 1 / 4^7
= 1 / (4*4*4*4*4*4*4)
= 1 / 16384
= 0.000061035

Now let's multiply this result by 49:

49 * 0.000061035 ≈ 0.00299

Therefore, the numerical equivalent of 49⋅4^(-7) is approximately 0.00299.

Answer 23

To find the numerical equivalent of 4^9⋅4^−7, we can apply the rule of exponents, which states that when multiplying two exponents with the same base, we add the exponents.

Therefore, 4^9 ⋅ 4^−7 can be simplified as 4^(9-7), which is equal to 4^2.

Using the definition of exponentiation, we know that 4^2 equals 4 * 4 = 16.

Hence, the numerical equivalent of 4^9 ⋅ 4^−7 is 16.