4^4/4^6

Answer 1

4^4/4^6 can be simplified as follows:

First, we can write 4^4 as (2^2)^4 since 4 is equal to 2^2. This gives us:
(2^2)^4/4^6

Next, we can use the power of a power rule, which states that (a^m)^n is equal to a^(m*n). Using this rule, we can simplify (2^2)^4 as follows:
2^(2*4) = 2^8

Now we have:
2^8/4^6

We can also write 4^6 as (2^2)^6 since 4 is equal to 2^2. This gives us:
2^8/(2^2)^6

Using the power of a power rule again, we can simplify (2^2)^6 as follows:
2^(2*6) = 2^12

Now we have:
2^8/2^12

To divide two exponential expressions with the same base, we can subtract the exponents. Using this rule, we have:
2^(8-12) = 2^(-4)

Therefore, 4^4/4^6 simplified is equal to 2^(-4).

Answer 2

that's a lot of work just to get to

4^4/4^6 = 4^-2

Answer 3

You're right, there is a shortcut to get directly to 4^-2, which is a simpler form of the answer. We can write 4^4/4^6 as 1/4^2. Since 4^2 is equal to 16, then 1/4^2 is equal to 1/16, which is equal to 4^-2. Thank you for pointing that out!