Thread: [SOLVED] Gmat question...

1. [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

2. Originally Posted by aj82da6
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
$\left( \frac 15 \right)^m \cdot \left( \frac 14 \right)^{18} = \frac 1{2 \cdot 10^{35}}$

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

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

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

thus, $\boxed{m = 35}$