Question 1204752
<pre>
Here's what to do in an EMERGENCY, but only in an EMERGENCY,
and only on a multiple-choice test where you don't have to
show your work.

If you run into a problem like this on a multiple-choice 
test and don't know what to do, and are completely stuck, 
then here is a trick that works a lot of the time. Some other
tutors here will frown on me for telling you this, but it 
works sometimes on certain problems. 

Substitute x=0.

Then 6^(2*0+1) = 6 = k, then 6^(4*0+3) = 6^3 = 216 

Then substitute 6 for k in every one of the choices:

A) 12k = 12(6) = 72
That's not 216, so that eliminates A

B) k^2 + 6 = (6)^2 + 6 = 42
That's not 216, so that eliminates B 

C) 6k^2 = 6(6)^2 = 6(36) = 216  
That IS 216, but that only means it's POSSIBLY the right choice.
For it happens sometimes that one of the others will also be 216.

D) 2k + 6 = 2(6) + 6 = 18.
That's not 216, so that eliminates D

E) 36k^2 = 36(6)^2 = 1296
That's not 216, so that eliminates E

So we know the correct choice is C.

If another one of them had also come out 216, then
you could do it again by substituting x=1 or x=-1. 
But if you're short on time, you still have a better 
chance of guessing correctly.

Also sometimes, on some problems, substituting 0 in what's
given and then in all the choices is the easiest method!
Sometimes you can do it in your head! I have actually used 
it myself to save time even though I knew how to get the 
solution the regular way! 

As I mentioned above, sometimes substituting 1 or -1 is 
better than 0.  Sometimes substituting 0 causes a denominator 
to be 0. Other times other numbers work better. So you can
improvise on this method.  But I'd better warn you, you'd
better not rely on this method!  It won't save you if you
don't understand the material! 

Edwin</pre>