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.
Use the Product Rule of Exponents to simplify the expression 75 ⋅72.(1 point)
23 answers
Find the numerical equivalent of 72⋅73(1 point)
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.
72⋅73 = 5256
Therefore, the numerical equivalent of 72⋅73 is 5256.
wrong
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.
72⋅73 = 5256
Therefore, the numerical equivalent of 72⋅73 is indeed 5256.
Find the numerical equivalent of 7^2⋅7^3(1 point)
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.
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.
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
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
The correct expression that can be developed to use the Product Rule of Exponents is: 62⋅73 (6 squared times 7 cubed).
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
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
The correct expression that can be developed to use the Product Rule of Exponents is: 6^2⋅7^3 (6 squared times 7 cubed).
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
Responses
20015
200 superscript 15 baseline
10056
100 superscript 56 baseline
10015
100 superscript 15 baseline
10,00015
10,000 superscript 15 baseline
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).
1008 ⋅ 1007 = 10^3 ⋅ 10^2 = 10^(3+2) = 10^5
Therefore, the correct answer is 10015 (100 superscript 15 baseline).
Find the numerical equivalent of 102 ⋅103(1 point)
Responses
100,000
100,000
10
10
1,100
1,100
105
Responses
100,000
100,000
10
10
1,100
1,100
105
To find the numerical equivalent of 102 ⋅ 103, we perform the multiplication.
102 ⋅ 103 = 1000
Therefore, the correct response is 1000.
102 ⋅ 103 = 1000
Therefore, the correct response is 1000.
Find the numerical equivalent of 102 ⋅103(1 point)
Responses
100,000
100,000
10
10
1,100
1,100
10^5
Responses
100,000
100,000
10
10
1,100
1,100
10^5
To find the numerical equivalent of 102 ⋅103, we perform the multiplication.
102 ⋅ 103 = 1000
Therefore, the correct response is 1000.
102 ⋅ 103 = 1000
Therefore, the correct response is 1000.
Find the numerical equivalent of 2^5 ⋅2^−2(1 point)
Responses
128
128
2
2
16
16
8
Responses
128
128
2
2
16
16
8
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.
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.
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
Question
Find the numerical equivalent of 49⋅4−7(1 point)
Responses
16
16
416
4 superscript 16 baseline
42
4 squared
4
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.
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.
Find the numerical equivalent of 4^9⋅4^−7(1 point)
Responses
16
16
416
4 superscript 16 baseline
42
4 squared
4
Responses
16
16
416
4 superscript 16 baseline
42
4 squared
4
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.
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.
1 answer