Write (3x)(3x)(3x)(3x) as a single exponent.
Why is this (3x) to the fourth power and not (81x) to the 4th power?
Its 3^4 because you count the times you are multiplying it.
But why don't you multiply all the 3's together?
(3x)(3x)(3x)(3x) = 81x^4
Uh well that didnt help i guess im on the wrong thing-
To simplify the expression (3x)(3x)(3x)(3x), you can use the exponent rule that states, when you multiply two powers with the same base, you add their exponents. In this case, the base is 3x and the exponents are 1 for each occurrence of (3x).
So, (3x)(3x)(3x)(3x) can be written as (3x)^1 * (3x)^1 * (3x)^1 * (3x)^1.
Using the exponent rule, we add the exponents:
(3x)^1 * (3x)^1 * (3x)^1 * (3x)^1 = (3x)^(1+1+1+1).
Simplifying further, we get:
(3x)^(1+1+1+1) = (3x)^4.
Now, let's address the second part of your question. It is not correct to write (3x)(3x)(3x)(3x) as (81x)^4 because the exponent rule mentioned earlier only applies when you have powers with the same base.
In (3x)(3x)(3x)(3x), the base is 3x, not 81x. The expression (3x) to the fourth power means that we are multiplying four copies of 3x together, rather than raising 81x to the fourth power, which would imply multiplying 81x by itself four times.