Video Explanation

Text Explanation

To solve this problem, it is very helpful to express all of the quantities in terms of the same base.  Once we do that, we can make use of the various Laws of Exponents to simplify the quantities further.

First, we'll express all of the quantities in terms of the same base of 2:

We can now simplify all the powers that are being raised to a power via this Law of Exponents:

(x^a)^b = x^ab

Next, we can simplify the numerator via this Law of Exponents:

(x^a) × (x^b) = x^{(a + b)}

We can then simplify the entire fraction via this Law of Exponents:

Lastly, we'll use the following rule to solve for n:

"If two powers with the same base are equal, then the exponents must be equal.  That is, if b^x = b^y, then x = y, provided that b does not equal 0 or +/– 1."

27 – 4n = 5 – 5n
n = 5 – 27
n = –22