(1/36)^w+2 < (1/216)^4w

(1/36)^(w+2) = (1/216)^(4w

did you realize that 36 = 6^2 and 216= 6^3

(1/6^2)^(w+2) < (1/6^3)^(4w)
6^(-2(w+2)) < 6^(-3(4w))
6^(-2w-4) < 6^(-12w)

then -2w-4 < -12w
10w < 4
w < 4/10 or
w < 2/5 or .4

To solve the inequality (1/36)^w+2 < (1/216)^4w, we need to compare the exponents of the bases 1/36 and 1/216.

Starting with the left side of the inequality, we can rewrite (1/36)^w+2 as (1/36)^(w+2). Similarly, the right side can be rewritten as (1/216)^(4w).

Now, since both sides have the same base (1/36 and 1/216), we can compare the exponents.

w + 2 < 4w

Next, we need to solve this inequality for w. Let's isolate the variable w on one side:

2 < 3w

Dividing both sides by 3 gives us:

2/3 < w

So, the solution to the inequality (1/36)^w+2 < (1/216)^4w is w > 2/3.