Question

Find the numerical equivalent of 10^2 ⋅10^3
A.1,100
B.10
C.100,000
D.10^5
Answer
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Answer
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Answer
Find the numerical equivalent of 2^5 ⋅2^−2(1 point)
Responses

8
8

16
16

128
128

2
Answer
Find the numerical equivalent of 49⋅4−7(1 point)
Responses

A.4
B.4^2
C.4^16
D.16
Answer
Find the numerical equivalent of 4^9⋅4^−7(1 point)
Responses

A.4
B.4^2
C.4^16
D.16

Answer
You are wrong
Answered by GPT 3.5
The numerical equivalent of 10^2 ⋅10^3 can be found by multiplying the exponents and keeping the base (10) raised to the sum of the exponents.

10^2 ⋅10^3 = 10^(2+3) = 10^5

Therefore, the numerical equivalent of 10^2 ⋅10^3 is 10^5.

The answer is option D. 10^5.
Answered by GPT 3.5
Apologies for the incorrect response earlier. Let's correct it:

The numerical equivalent of 10^2 ⋅ 10^3 is 10^(2+3) = 10^5 (as mentioned earlier).

Therefore, the correct answer is option D. 10^5.
Answered by GPT 3.5
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Answered by GPT 3.5
The numerical equivalent of 2^5 ⋅ 2^(-2) can be found by multiplying the bases (2) and adding the exponents.

2^5 ⋅ 2^(-2) = 2^(5 + (-2)) = 2^3

Therefore, the numerical equivalent of 2^5 ⋅ 2^(-2) is 8.

The answer is option A. 8.
Answered by GPT 3.5
To find the numerical equivalent of 49⋅4^(-7), we need to evaluate the exponent first and then perform the multiplication.

Starting with 4^(-7), the negative exponent indicates that we should take the reciprocal of the base raised to the positive exponent:

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

Now, we can multiply 49 by the result:

49⋅4^(-7) = 49 * 0.000061035 ≈ 0.002988525

The closest response option is D. 16, but none of the provided options accurately represents the numerical result.

Please note that this calculation may not yield an exact integer or a response option given in the provided multiple-choice options.
Answered by GPT 3.5
To find the numerical equivalent of 4^9⋅4^(-7), we can use the rule of exponents that states when you multiply two numbers with the same base, you add their exponents.

Starting with 4^9, we can keep the base (4) and add the exponents:

4^9 ⋅ 4^(-7) = 4^(9 + (-7))

Now, we can simplify the exponent:

4^(9 + (-7)) = 4^2

Therefore, the numerical equivalent of 4^9⋅4^(-7) is 4^2.

The answer is option B. 4^2.
Answered by GPT 3.5
Apologies for the mistake. Let's correct it:

When multiplying two numbers with the same base, you add their exponents. Using this rule, we can calculate the numerical equivalent of 4^9⋅4^(-7) as:

4^9 ⋅ 4^(-7) = 4^(9-7) = 4^2

So, the numerical equivalent of 4^9⋅4^(-7) is 4^2.

The answer is option B. 4^2.