Raise both sides by 3:

\(\displaystyle{n}^{{3}}={\left({3}\sqrt{{{6}\frac{{V}}{{7}}π}}\right)}^{{3}}\)

\(\displaystyle{n}^{{3}}={6}\frac{{V}}{{7}}π\)

Multiply both sides by 7π: \(\displaystyle{7}π{n}^{{3}}={\left({6}\frac{{V}}{{7}}π\right)}{\left({7}π\right)}\)

\(\displaystyle{7}π{n}^{{3}}={6}{V}\)

Divide both sides by 6: \(\displaystyle{7}π\frac{{n}^{{3}}}{{6}}={6}\frac{{V}}{{6}}\)

\(\displaystyle{7}π\frac{{n}^{{3}}}{{6}}={V}\)

or

\(\displaystyle{V}={7}π\frac{{{n}^{{3}}}}{{6}}\)

\(\displaystyle{n}^{{3}}={\left({3}\sqrt{{{6}\frac{{V}}{{7}}π}}\right)}^{{3}}\)

\(\displaystyle{n}^{{3}}={6}\frac{{V}}{{7}}π\)

Multiply both sides by 7π: \(\displaystyle{7}π{n}^{{3}}={\left({6}\frac{{V}}{{7}}π\right)}{\left({7}π\right)}\)

\(\displaystyle{7}π{n}^{{3}}={6}{V}\)

Divide both sides by 6: \(\displaystyle{7}π\frac{{n}^{{3}}}{{6}}={6}\frac{{V}}{{6}}\)

\(\displaystyle{7}π\frac{{n}^{{3}}}{{6}}={V}\)

or

\(\displaystyle{V}={7}π\frac{{{n}^{{3}}}}{{6}}\)