Question: Equation with Powers of 11

Comment on Equation with Powers of 11

I got the same result but with different approach. Just want to know if this works for any question I did not get the answer because of the number.
(11^6)(11^6)/(11^8)(11^4k)=1/(11^3)
(11^-2)(11^6-4k)=(11^-3) then I solved for k in the equation
-2+6-4k=-3
4k=6+3-2
k=7/4
greenlight-admin's picture

That works also!
All of your steps are perfectly sound, because you correctly applied the exponent rules.
Nice job!

If we had to guess, could we rule out all of the negative answers (A, B, and C) since k is in the denominator on the left side, and on the right side the exponent in the denominator is positive?
greenlight-admin's picture

That's a good idea, but that strategy won't always work.

Consider this equation: (2^-10)/(2^x) = 1/(2^7)
This has similar elements to the question in the video, so we might conclude (incorrectly) that x must be positive.

However, in this case, x = -3

Sorry if this is obvious, but I am confused about what happens at 1:03, getting 4 - 4k. Doesn't 12 - (8 + 4k) = 4 + 4k ? I am getting the answer - 7 / 4.
greenlight-admin's picture

12 - (8 + 4k) = 4 - 4k

We start with 12 (and zero k's).

From this amount, we're subtracting (8 + 4k)

That is, we're subtracting positive 8 AND we're subtracting positive 4k

12 MINUS 8 equals positive 4
zero k's MINUS 4k equals negative 4k

For more on this, start watching the following video at 3:58
https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Cheers,
Brent

Hi, why can't we cross multiply them?
I tried it, got the wrong answer but i would like to know why can't we cross-multiply?
greenlight-admin's picture

We can definitely cross multiply here.
Given: (11⁶)²/(11² x 11^k)⁴ = 1/11³
Cross multiply to get: (11⁶)²(11³) = (1)(11² x 11^k)⁴
Simplify the left side: 11¹⁵ = 11^(8 + 4k)
Since the bases are equal, the exponents must be equal.

So we have: 15 = 8 + 4k
Solve: k = 7/4

Ready for Test Day?

Try to achieve your target scores on at least two practice tests before taking the official test. 

Free “Question of the Day” emails!