We have to simplify the numerator of this fraction, . There are exponent rules for multiplying or dividing different powers of the same base, but there's no exponent rule for adding or subtracting powers of the same base.

Nevertheless, whenever we are adding or subtracting any two numbers or algebraic expressions, one option always open to us is to factor out the GCF of the two terms. This is one way in which we can simply the numerator of this problem.

We know that 4^{6} is six factors of 4 multiplied together, and 4^{5} is five factors of 4 multiplied together. What is their GCF? Their GCF is 4^{5}!

Now, we can use that simplified form in the prompt fraction:

Answer = (E)

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