Use the Product Rule of Exponents to simplify the expression 2 to the 4th power ⋅ 2 to the 2ed power
The Product Rule of Exponents states that for any two real numbers a and b, and any positive integer n, a to the n-th power multiplied by a to the b-th power equals a to the (n+b)-th power.
Applying the Product Rule of Exponents to the expression 2^4 * 2^2:
2^4 * 2^2 = 2^(4+2) = 2^6
Therefore, 2^4 * 2^2 simplifies to 2^6.
3 to the 8th power * 3 to the 3ed power
Using the Product Rule of Exponents, we can simplify the expression 3^8 * 3^3 as follows:
3^8 * 3^3 = 3^(8+3) = 3^11
Therefore, 3^8 * 3^3 simplifies to 3^11.
7 to the 5th power * 7 to the 2ed power
Using the Product Rule of Exponents, we can simplify the expression 7^5 * 7^2 as follows:
7^5 * 7^2 = 7^(5+2) = 7^7
Therefore, 7^5 * 7^2 simplifies to 7^7.
7 to the 2ed power * 7 to the 3ed power
Using the Product Rule of Exponents, we can simplify the expression 7^2 * 7^3 as follows:
7^2 * 7^3 = 7^(2+3) = 7^5
Therefore, 7^2 * 7^3 simplifies to 7^5.
Find the numerical equivalent of 7^2⋅7^3
To find the numerical equivalent of 7^2 * 7^3, we can simply calculate the exponentiation and multiplication:
7^2 * 7^3 = 49 * 343 = 16,807
Therefore, the numerical equivalent of 7^2 * 7^3 is 16,807.
Find the numerical equivalent of 3^9 ⋅ 3^−5
To find the numerical equivalent of 3^9 * 3^-5, we can calculate each exponentiation and then multiply the results:
3^9 * 3^-5 = 19683 * (1/243) = 0.08065
Therefore, the numerical equivalent of 3^9 * 3^-5 is approximately 0.08065.
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
327
32 superscript 7 baseline
62⋅73
6 squared times 7 cubed
108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline
The correct expression that utilizes the Product Rule of Exponents is:
(6^2) * (7^3)
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10056
100 superscript 56 baseline
20015
200 superscript 15 baseline
10,00015
10,000 superscript 15 baseline
10015
The correct expression that correctly uses the Product Rule of Exponents to simplify the expression 1008 * 1007 is:
1,015,056
Find the numerical equivalent of 102 ⋅103(1 point)
Responses
10
10
105
10 superscript 5 baseline
100,000
100,000
1,100
To find the numerical equivalent of 102 ⋅ 103, we can calculate each exponentiation and then multiply the results:
102 ⋅ 103 = 100 ⋅ 1,000 = 100,000
Therefore, the numerical equivalent of 102 ⋅ 103 is 100,000.
Find the numerical equivalent of 10^2 ⋅10^3 (1 point)
Responses
10
10
105
10 superscript 5 baseline
100,000
100,000
1,100
To find the numerical equivalent of 10^2 ⋅ 10^3, we can calculate each exponentiation and then multiply the results:
10^2 ⋅ 10^3 = 100 ⋅ 1,000 = 100,000
Therefore, the numerical equivalent of 10^2 ⋅ 10^3 is 100,000.
Find the numerical equivalent of 2^5 ⋅2^−2(1 point)
Responses
16
16
8
8
2
2
128
To find the numerical equivalent of 2^5 ⋅ 2^-2, we can calculate each exponentiation and then multiply the results:
2^5 ⋅ 2^-2 = 32 ⋅ 1/4 = 32/4 = 8
Therefore, the numerical equivalent of 2^5 ⋅ 2^-2 is 8.
Find the numerical equivalent of 4^9⋅4^−7(1 point)
Responses
416
4 superscript 16 baseline
16
16
42
4 squared
4
4
To find the numerical equivalent of 4^9 * 4^-7, we can calculate each exponentiation and then multiply the results:
4^9 * 4^-7 = 262,144 * 1/16 = 262,144/16 = 16,384
Therefore, the numerical equivalent of 4^9 * 4^-7 is 16,384.
Find the numerical equivalent of 4^9 ⋅ 4^−7 (1 point)
Responses
4 superscript 16 baseline
16
4 squared by 2
4
To find the numerical equivalent of 4^9 ⋅ 4^−7, we can calculate each exponentiation and then multiply the results:
4^9 ⋅ 4^-7 = 262,144 ⋅ 1/16 = 262,144/16 = 16,384
Therefore, the numerical equivalent of 4^9 ⋅ 4^−7 is 16,384.