I need help with this problem from my practice gmat..

(1/5)^m times (1/4)^18 = 1/(2(10)^35)

and we are trying to find m

thank you for your help

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- Feb 7th 2008, 06:27 PMaj82da6[SOLVED] Gmat question...
I need help with this problem from my practice gmat..

(1/5)^m times (1/4)^18 = 1/(2(10)^35)

and we are trying to find m

thank you for your help - Feb 7th 2008, 07:08 PMJhevon
$\displaystyle \left( \frac 15 \right)^m \cdot \left( \frac 14 \right)^{18} = \frac 1{2 \cdot 10^{35}}$

$\displaystyle \Rightarrow \left( \frac 15 \right) \cdot \frac 1{2^{36}} = \frac 1{2 (2 \cdot 5)^{35}}$

$\displaystyle \Rightarrow \left( \frac 15 \right)^m \cdot \frac 1{2^{36}} = \frac 1{2^{36} \cdot 5^{35}}$

$\displaystyle \Rightarrow \left( \frac 15 \right)^m = \frac 1{5^{35}}$

thus, $\displaystyle \boxed{m = 35}$