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m and n are integers.
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07 Dec 2017, 03:16
07 Dec 2017, 03:16
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m and n are integers.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\((\sqrt{10^{2m}})(\sqrt{10^{2n}})\) |
\(10^{mn}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
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Re: m and n are integers.
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08 Dec 2017, 10:59
08 Dec 2017, 10:59
5
Carcass wrote:
m and n are integers.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\((\sqrt{10^{2m}})(\sqrt{10^{2n}})\) |
\(10^{mn}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
RULE: √x = x^(1/2)
So, √[10^(2m)] = [10^(2m)]^(1/2)
= 10^m [once we apply the Power of a Power rule]
Likewise, √[10^(2n)] = [10^(2n)]^(1/2)
= 10^n [once we apply the Power of a Power rule]
We get:
QUANTITY A: (10^m)(10^n)
QUANTITY B: 10^(mn)
Simplify to get:
QUANTITY A: 10^(m+n)
QUANTITY B: 10^(mn)
Let's test some values of m and n
m = 0 and n = 0
We get:
QUANTITY A: 10^(0+0) = 10^0 = 1
QUANTITY B: 10^[(0)(0)] = 10^0 = 1
In this case the two quantities are equal
m = 1 and n = 1
We get:
QUANTITY A: 10^(1+1) = 10^2 = 100
QUANTITY B: 10^[(1)(1)] = 10^1 = 10
In this case Quantity is greater
Answer: D
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