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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]
06 Aug 2014, 17:12

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Re: If (1/5)^m * (1/4)^18 = 1/(2*(10)^35), then m = ? [#permalink]
06 Aug 2014, 17:36

This question does not require any calculation as such. On comparing powers of primes between LHS and RHA, we find that RHS has 2^35 (10^35=(2*5)^35) so m has to be 35

Shortcut approach: \((\frac{1}{5})^m * (\frac{1}{4})^{18} = \frac{1}{2*10^{35}}\) --> \(\frac{1}{5^m}* (\frac{1}{4})^{18} = \frac{1}{2*2^{35}*5^{35}}\) --> as there are only integers in the answer choices then we can concentrate only on the power of 5: they should be equal on both sides --> \(m=35\).

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