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16 Sep 2014, 00:39
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If \(\frac{25}{\frac{x}{5}} = \frac{\frac{1}{25}}{125}\), then \(x =\)?
A. \(5^{-2}\)
B. \(5^2\)
C. \(5^4\)
D. \(5^8\)
E. \(5^{10}\)
A. \(5^{-2}\)
B. \(5^2\)
C. \(5^4\)
D. \(5^8\)
E. \(5^{10}\)
16 Sep 2014, 00:39
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Bookmarks
Official Solution:
If \(\frac{25}{\frac{x}{5}} = \frac{\frac{1}{25}}{125}\), then \(x =\)?
A. \(5^{-2}\)
B. \(5^2\)
C. \(5^4\)
D. \(5^8\)
E. \(5^{10}\)
Given: \(\frac{25}{\frac{x}{5}} = \frac{\frac{1}{25}}{125}\):
By cross-multiplying, we get: \(25 * 125 = \frac{x}{5} * \frac{1}{25}\).
Cross-multiplying both sides again, we find: \(25 * 125 * 5 * 25 = x\).
When expressed in powers of 5, this becomes: \(5^2 * 5^3 * 5 * 5^2 = x\).
Therefore, \(x = 5^8\).
Answer: D
If \(\frac{25}{\frac{x}{5}} = \frac{\frac{1}{25}}{125}\), then \(x =\)?
A. \(5^{-2}\)
B. \(5^2\)
C. \(5^4\)
D. \(5^8\)
E. \(5^{10}\)
Given: \(\frac{25}{\frac{x}{5}} = \frac{\frac{1}{25}}{125}\):
By cross-multiplying, we get: \(25 * 125 = \frac{x}{5} * \frac{1}{25}\).
Cross-multiplying both sides again, we find: \(25 * 125 * 5 * 25 = x\).
When expressed in powers of 5, this becomes: \(5^2 * 5^3 * 5 * 5^2 = x\).
Therefore, \(x = 5^8\).
Answer: D
19 Oct 2023, 11:18
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
