Given that the point \((6, 1)\) lies on the graph of the function \(h(x) = \log_6 x\), it means that:
\[ h(6) = 1 \quad \Rightarrow \quad \log_6 6 = 1 \]
Now, to find a corresponding point on the graph of the function \(k(x) = 6^x\), we can use the properties of logarithms and exponentials.
If \(h(x) = \log_6 x\), then by definition of logarithms, we have:
\[ x = 6^{h(x)} \]
In this case, since \(h(6) = 1\):
- We can write \(6 = 6^{h(6)} = 6^1\).
This means that when \(x = 1\), the value of the function \(k(x) = 6^x\) is:
\[ k(1) = 6^1 = 6 \]
Thus, the point \((1, 6)\) can be deduced.
Therefore, the point \((1, 6)\) is guaranteed to be on the graph of the function \(k(x) = 6^x\).