Question 1135939
216^-2k
-------- = 36   Please show steps and solution.
36^-2k-3
<pre>If {{{matrix(1,3, 216^(- 2k)/36^(- 2k - 3), "=", 36)}}}, then:
{{{matrix(1,3, (6^3)^(- 2k)/(6^2)^(- 2k - 3), "=", 6^2)}}}
{{{matrix(1,3, 6^(- 6k)/6^(- 4k - 6), "=", 6^2)}}}
{{{matrix(1,3, 6^(- 6k - (- 4k - 6)), "=", 6^2)}}} ----- Applying {{{matrix(1,3, a^b/a^c, "=", a^(b - c))}}}
- 6k - (- 4k - 6) = 2 ------- Bases are equal and so are the exponents
- 6k + 4k + 6 = 2
- 2k = 2 - 6
- 2k = - 4
{{{highlight_green(matrix(1,5, k, "=", (- 4)/(- 2), "=", 2))}}}
You DON'T NEED LOGS or any complex calculations....just the laws of exponents! 
Using logs is just a waste of time and effort, unless you're requested to use logs, of course.