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If xy = 1 and x is not equal to y, then what is the value of [m](7 ^{(
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15 Feb 2022, 07:01
15 Feb 2022, 07:01
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If xy = 1 and x is not equal to y, then what is the value of \((7 ^{(\frac{1}{x-y})})^{(\frac{1}{x}- \frac{1}{y})}\)?
A. \(\frac{1}{49}\)
B. \(\frac{1}{7}\)
C. 1
D. 7
E. 49
A. \(\frac{1}{49}\)
B. \(\frac{1}{7}\)
C. 1
D. 7
E. 49
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Re: If xy = 1 and x is not equal to y, then what is the value of [m](7 ^{(
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15 Feb 2022, 07:29
15 Feb 2022, 07:29
Carcass wrote:
If xy = 1 and x is not equal to y, then what is the value of \((7 ^{(\frac{1}{x-y})})^{(\frac{1}{x}- \frac{1}{y})}\)?
A. \(\frac{1}{49}\)
B. \(\frac{1}{7}\)
C. 1
D. 7
E. 49
A. \(\frac{1}{49}\)
B. \(\frac{1}{7}\)
C. 1
D. 7
E. 49
Let's first simplify the exponent \(\frac{1}{x}- \frac{1}{y}\)
\(\frac{1}{x}- \frac{1}{y}=\frac{y}{xy}- \frac{x}{xy}=\frac{y-x}{xy}\)
So we get: \((7 ^{(\frac{1}{x-y})})^{(\frac{1}{x}- \frac{1}{y})}=(7 ^{(\frac{1}{x-y})})^{(\frac{y-x}{xy})}\)
Apply the power of a power law: \(=7 ^{(\frac{1}{x-y})(\frac{y-x}{xy})}\)
Simplify: \(=7 ^{(\frac{-1}{xy})}\)
Substitute \(1\) for \(xy\) to get: \(=7 ^{(\frac{-1}{1})} = 7^{-1}=\frac{1}{7}\)
Answer: B
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Re: If xy = 1 and x is not equal to y, then what is the value of [m](7 ^{( [#permalink]
15 Feb 2022, 07:29
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