I have a situation like this:
$3\times 10^n$ and $4\times 10^m$ and $a\times 10^p$ are all in standard form. $$\frac{3\times 10^n}{4\times 10^m} = a\times 10^p.$$
Is it possible to calculate the value of $a$ only by using the above equation and no further data? And if so what is the value of $a$?
You have $$\frac{3\times 10^n}{4\times 10^m} = 0.75\times 10^{n-m}.$$ If by "standard form" you mean that the the number $a$ must be between $1$ and $10$, strictly less than $10$, then $a = 7.5$ with $p=n-m+1$