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
$\displaystyle \left( \frac 15 \right)^m \cdot \left( \frac 14 \right)^{18} = \frac 1{2 \cdot 10^{35}}$
$\displaystyle \Rightarrow \left( \frac 15 \right) \cdot \frac 1{2^{36}} = \frac 1{2 (2 \cdot 5)^{35}}$
$\displaystyle \Rightarrow \left( \frac 15 \right)^m \cdot \frac 1{2^{36}} = \frac 1{2^{36} \cdot 5^{35}}$
$\displaystyle \Rightarrow \left( \frac 15 \right)^m = \frac 1{5^{35}}$
thus, $\displaystyle \boxed{m = 35}$