Indicate what is the base of the exponential functions that satisfy the following relations. Indicate, also, its domain and image:
 $$f(2)=16$$
 $$h(2)=25$$
 $$\displaystyle g(3)=\frac{1}{64}$$
See development and solution
Development:

To find the base of the exponential function we raise and solve the following equation: $$$x^2=16 \Rightarrow x=4$$$ Therefore $$4$$ is the base of the function, with $$Dom (f) = \mathbb{R}$$ and $$Im (f) = (0,+\infty)$$.

We proceed as in the previous case: $$$x^{2}=25 \Rightarrow x^2=\dfrac{1}{25} \Rightarrow x=\dfrac{1}{5}$$$ Therefore the base of the function is $$\dfrac{1}{5}$$, with $$Dom (f) = \mathbb{R}$$ and $$Im (f) = (0,+\infty)$$.
 We proceed as in the previous case: $$$x^3=\dfrac{1}{64} \Rightarrow x=\sqrt[3]{\dfrac{1}{64}} \Rightarrow x=\dfrac{1}{4}$$$ Therefore the base of function is $$\dfrac{1}{4}$$, with $$Dom (f) =\mathbb{R}$$ and $$Im (f) = (0,+\infty)$$.
Solution:
 $$b=4$$, $$Dom (f) = \mathbb{R}$$, $$Im (f) = (0,+\infty)$$
 $$b=\dfrac{1}{5}$$, $$Dom (f) = \mathbb{R}$$, $$Im (f) = (0,+\infty)$$
 $$b=\dfrac{1}{4}$$, $$Dom (f) =\mathbb{R}$$, $$Im (f) = (0,+\infty)$$