Simplify \({3}^{4}\) to \(81\).
\[81\times {9}^{2}={3}^{n}thenn\]
Simplify \({9}^{2}\) to \(81\).
\[81\times 81={3}^{n}thenn\]
Simplify \(81\times 81\) to \(6561\).
\[6561={3}^{n}thenn\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[6561={3}^{n}the{n}^{2}\]
Regroup terms.
\[6561=eth{n}^{2}\times {3}^{n}\]
Divide both sides by \(e\).
\[\frac{6561}{e}=th{n}^{2}\times {3}^{n}\]
Divide both sides by \(t\).
\[\frac{\frac{6561}{e}}{t}=h{n}^{2}\times {3}^{n}\]
Simplify \(\frac{\frac{6561}{e}}{t}\) to \(\frac{6561}{et}\).
\[\frac{6561}{et}=h{n}^{2}\times {3}^{n}\]
Divide both sides by \({n}^{2}\).
\[\frac{\frac{6561}{et}}{{n}^{2}}=h\times {3}^{n}\]
Simplify \(\frac{\frac{6561}{et}}{{n}^{2}}\) to \(\frac{6561}{et{n}^{2}}\).
\[\frac{6561}{et{n}^{2}}=h\times {3}^{n}\]
Divide both sides by \({3}^{n}\).
\[\frac{\frac{6561}{et{n}^{2}}}{{3}^{n}}=h\]
Simplify \(\frac{\frac{6561}{et{n}^{2}}}{{3}^{n}}\) to \(\frac{6561}{et{n}^{2}\times {3}^{n}}\).
\[\frac{6561}{et{n}^{2}\times {3}^{n}}=h\]
Switch sides.
\[h=\frac{6561}{et{n}^{2}\times {3}^{n}}\]
h=6561/(e*t*n^2*3^n)
