Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
10^8 ⋅ 10^8
(5^2)^9
6^2 ⋅ 7^3
32^7
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The correct expression that uses 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 100^8⋅100^7?(1 point)
Responses
100^56
10,000^15
100^15
200^15
The correct expression that applies the Product Rule of Exponents to simplify 100^8⋅100^7 is 100^15.
Find the numerical equivalent of 10^2 ⋅10^3(1 point)
Responses
100,000
10
1,100
10^5
The numerical equivalent of 10^2 ⋅ 10^3 is 10^5, which is equal to 100,000.
Find the numerical equivalent of 2^5 ⋅ 2^−2(1 point)
Responses
16
128
2
8
To find the numerical equivalent of 2^5 ⋅ 2^−2, we can simplify each term separately and then multiply them together.
2^5 = 2 * 2 * 2 * 2 * 2 = 32
2^−2 = 1 / (2 * 2) = 1/4 = 0.25
Now, we can multiply the simplified terms:
32 * 0.25 = 8
Therefore, the numerical equivalent of 2^5 ⋅ 2^−2 is 8.
Find the numerical equivalent of 4^9 ⋅ 4^−7(1 point)
Responses
4
4^2
16
4^16
To find the numerical equivalent of 4^9 ⋅ 4^−7, we can simplify each term separately and then multiply them together.
4^9 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 262,144
4^−7 = 1 / (4 * 4 * 4 * 4 * 4 * 4 * 4) = 1 / 16384 = 0.000061035
Now, we can multiply the simplified terms:
262,144 * 0.000061035 ≈ 16
Therefore, the numerical equivalent of 4^9 ⋅ 4^−7 is approximately 16.