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a, b, and c are integers greater than 1
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15 Feb 2022, 02:34
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a, b, and c are integers greater than 1 and \((c^b)^{5}=c^{5+a}\)
Quantity A
Quantity B
\(a\)
\(b\)
A) The quantity in Column A is greater. B) The quantity in Column B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
a, b, and c are integers greater than 1
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15 Feb 2022, 07:24
1
Carcass wrote:
a, b, and c are integers greater than 1 and \((c^b)^{5}=c^{5+a}\)
Quantity A
Quantity B
\(a\)
\(b\)
A) The quantity in Column A is greater. B) The quantity in Column B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
Given: \((c^b)^{5}=c^{5+a}\)
Apply the Power of a Power law to the left side to get: \(c^{5b}=c^{5+a}\)
Since the bases are equal, the exponents must be equal: \(5b = 5 + a\)
Subtract \(5\) from both sides to get: \(5b - 5 = a\)
Take Quantity A and replace \(a\) with \(5b - 5\) to get: QUANTITY A: \(5b - 5\) QUANTITY B: \(b\)
From here, we can solve the question using a technique called matching operations. See the video below.
Subtract \(b\) from both quantities: QUANTITY A: \(4b - 5\) QUANTITY B: \(0\)
Add \(5\) to both quantities: QUANTITY A: \(4b\) QUANTITY B: \(5\)
Divide both quantities by \(4\): QUANTITY A: \(b\) QUANTITY B: \(1.25\)
Since we are told that \(b\) is an INTEGER greater than 1, quantity A must be greater then quantity B