One thing that always confuses me about exponent is that how to visualize it. Suppose we have
$$2^3$$ This means that we multiply 2 three times $2^3 = 2\times2\times2$
But what if the exponent is a decimal such as $2^{2.345}$ Does this mean that we must multiply 2 2.345 times ? I'm confused on how to represent this
Suppose that we have a number $x$ such that $x^{2} = a$ where $a$ is something finite. Then, we can let $x = a^{\large\frac{1}{2}}$. Now, assume that we have a number $x$ such that $x^{n} = a$ where $n \in \mathbb{N}$. We can let $$x = a^{\large\frac{1}{n}}.$$
Now, we can raise $x$ to an arbitrary power $m$ such that $$x^{m} = a^{\large\frac{m}{n}}.$$
In your case, the exponent is $2.345$ and is equal to $\frac{469}{200}$. Hence, $$2^{2.345} = \sqrt[\large200]{2^{469}}.$$