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# If 25/(x/5) = (1/25)/125 then x = ?

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Re: If 25/(x/5) = (1/25)/125 then x = ? [#permalink]
Bunuel wrote:
If $$\frac{25}{(\frac{x}{5})} = \frac{(\frac{1}{25})}{125}$$ then x = ?

(A) 5^(-2)

(B) 5^2

(C) 5^3

(D) 5^8

(E) 5^11

If we multiply the left side of the equation by 5/5 and the right side of the equation by 25/25, we have:

125/x = 1/(25 * 125)

Cross-multiplying, we obtain:

x = 125 * 25 * 125 = 5^3 * 5^2 * 5^3 = 5^8

Math Expert
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Re: If 25/(x/5) = (1/25)/125 then x = ? [#permalink]
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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. $$5^{10}$$

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, $$x = 5^8$$.