Function to grab specific digits from a number?
Recently I’ve been thinking a lot about grabbing digits from numbers, for things like calculating multiplication persistence, i.e. turning $1234$ into a ${\displaystyle 1\times 2\times 2\times 3\times 4}$. I’ve been able to come up with
${\displaystyle \left[\log x\right]+1}$
to output the number of digits of the given number x, as well as
$\lfloor \frac{x}{{10}^{\lfloor \log x\rfloor -n+1}}\rfloor$
which outputs the first n digits of any number x. But that’s about as far as I’ve been able to think up. Is there any way to construct a function that retrieves the nth digit of a given number? Forgive me if my notation or comprehension is poor, I have no formal education in this field of maths.

A cone has a height of 6 yards and a radius of 3 yards. What is its volume?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

a family has three children find the values of the random variable x representing the number of girls and construct a probability distribution

Find the equation of quadratic function given that the zeros are -3/4 and 5/6.

Logarithm rules, which one has priority? ${\displaystyle \ln 2e^{2x}}$
${\displaystyle \ln 2e^{2x}}$
Here are the two results I came up with:
${\displaystyle 2x\left(\ln 2e\right)}$
${\displaystyle 2x(\ln 2+\ln e)}$
$2x(\ln 2+1)$
$2x\ln 2+2x$
and
${\displaystyle \ln 2+{\ln e}^{2x}}$
${\displaystyle \ln 2+2x\ln e}$
I am sort of leaning towards the first result I got but I am not really sure. Could someone explain whether or not it is correct? I have looked at the log rules but I cannot recall which ones have priority over others.

Des