MHB [ASK] find abc if a^2bc^3=5^3 and ab^2=5^6

[Monoxdifly]

If $$a^2bc^3=5^3$$ and $$ab^2=5^6$$, what does abc equal to? I'm stuck and always getting 0 = 0 or c = c.

 

[Prove It]

If $$a^2bc^3=5^3$$ and $$ab^2=5^6$$, what does abc equal to? I'm stuck and always getting 0 = 0 or c = c.

I have a feeling that you must have been told $\displaystyle \begin{align*} a\,c^2 = 5^6 \end{align*}$, not $\displaystyle \begin{align*} a\,b^2 \end{align*}$. Assuming that I am right...

$\displaystyle \begin{align*} a^2\,b\,c^3 &= 5^3 \\ a\,c^2\left( a\,b\,c \right) &= 5^3 \\ a\,b\,c &= \frac{5^3}{a\,c^2} \\ a\,b\,c &= \frac{5^3}{5^6} \\ a\,b\,c &= \frac{1}{5^3} \\ a\,b\,c &= \frac{1}{125} \end{align*}$