Great question! To find the value of k, let's start by rearranging the equation. We have 1 divided by h(x), which is equal to 2 raised to the power of kx.
To simplify this, we can rewrite 2^(kx) as (2^k)^x using the exponent rule. Now our equation becomes 1/h(x) = (2^k)^x.
Since the bases on both sides of the equation are equal, the exponents must also be equal. Therefore, kx = 1 and we can isolate k by dividing both sides of the equation by x.
This gives us k = 1/x.
So, the value of k in the equation 1/(h(x)) = 2^(kx) is 1/x.
If you have any more questions or need further clarification, feel free to ask!