How to find an algebraic term when 2 similar exponential forms of it are given?

Question

if $a^2bc^3 = 25$ and $ab^2= 5$, how would you find $abc$?

Is there a formula of which these are a part of? What I've done is this:

$$abc^3 = \frac{25}a\quad\implies\quad abc = \frac{25}{ac^2}$$

But how would I use the $ab^2$?

Answer 1

Note that $\left(a^2bc^3\right)\left(ab^2\right)=a^3b^3c^3=(abc)^3$. Can you finish it from here?