4^4/4^6
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).
that's a lot of work just to get to
4^4/4^6 = 4^-2
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!
To simplify the expression 4^4 / 4^6, we can start by applying the rule of exponents for division. According to the rule, when dividing two exponents with the same base, we subtract the exponents.
So, let's calculate:
4^4 / 4^6 = 4^(4-6)
Now, we simplify the exponent:
4^(4-6) = 4^(-2)
To further simplify, we can use another rule of exponents, which states that any number (except 0) raised to the power of -n is equal to 1 divided by that number raised to the power of n.
Applying this rule, we rewrite 4^(-2) as:
4^(-2) = 1 / 4^2
Now, we calculate:
1 / 4^2 = 1 / 16
Therefore, the simplified expression 4^4 / 4^6 is equal to 1/16.