4^4/4^6

Question

(btw these are called polynomials
A. -16
B. 16
C. 1/16
D. -1/16

I understand how to work with polynomials, but I've never seen a question like this. I feel like it's A. Can someone please explain how I would do this

Answer 1

4^4 / 4^6
One way to solve this is to expand the numerator and denominator and simplify the fraction to its lowest term.

Another way to solve this is to apply some laws of exponent. We can see here that the numerator and denominator has a term with the same base (which is 4). When terms with the same base raised to some exponent are divided, we can rewrite it such that the base is raised to the difference of the exponents. Applying this to our expression,
4^4 / 4^6
= 4^(4 - 6)
= 4^(-2)

When a term is raised by a negative exponent, we can rewrite it such that its exponent is positive but it becomes the reciprocal:
4^(-2)
= 1 / (4^2)
= 1 / 16

Hope this helps~ `u`