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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.

Since you are asked to find the power of 5 i.e. m, you should be looking for 5 on the right hand side of the equation raised to some power. There is 10 on the denominator which is 2 * 5 raised to the power 35. The rest of the solution is rearranging to compare the powers of 5 on both sides. _________________

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Last edited by hb on 10 Aug 2013, 19:07, edited 1 time in total.

If (1/5)^m * (1/4)^18 = 1/(2(10)^35), then m = ? [#permalink]
23 Aug 2014, 22:26

Just need to break the equations a bit: 1. (1/5)^m (1/4)^18 = (1/5)^m (1/2)^36 = so now we have 36 powers of 1/2 and need to find for 5 , what we need is the relation between this equation and other so we will try to sync them up. 2. 1/(2(10)^35) = 1/(2(2*5)^35 = so now we have 36 powers of 2 and 35 powers of 5 Finally what we need is how many powers of 5?? its 35 , OA:D. Hope its clear _________________

Comparing left and right side (1/2)^36 is same on both sides . For equation to be true (1/5)^35 should equal to (1/5)^m which is possible when m=35 _________________