Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[Determ\imath ne\times {8}^{x}{x}^{x}\imath f\times {9}^{x+2}=240+{9}^{x}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[Det{e}^{2}rm{\imath }^{2}n\times {8}^{x}{x}^{x}f\times {9}^{x+2}=240+{9}^{x}\]
Use Square Rule: \({i}^{2}=-1\).
\[Det{e}^{2}rm\times -1\times n\times {8}^{x}{x}^{x}f\times {9}^{x+2}=240+{9}^{x}\]
Simplify \(Det{e}^{2}rm\times -1\times n\times {8}^{x}{x}^{x}f\times {9}^{x+2}\) to \(Det{e}^{2}rm\times -n\times {8}^{x}{x}^{x}f\times {9}^{x+2}\).
\[Det{e}^{2}rm\times -n\times {8}^{x}{x}^{x}f\times {9}^{x+2}=240+{9}^{x}\]
Regroup terms.
\[-De{e}^{2}trmn{x}^{x}f\times {8}^{x}\times {9}^{x+2}=240+{9}^{x}\]
Divide both sides by \(-De\).
\[{e}^{2}trmn{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{240+{9}^{x}}{De}\]
Divide both sides by \({e}^{2}\).
\[trmn{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{\frac{240+{9}^{x}}{De}}{{e}^{2}}\]
Simplify \(\frac{\frac{240+{9}^{x}}{De}}{{e}^{2}}\) to \(\frac{240+{9}^{x}}{De{e}^{2}}\).
\[trmn{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{240+{9}^{x}}{De{e}^{2}}\]
Divide both sides by \(r\).
\[tmn{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{\frac{240+{9}^{x}}{De{e}^{2}}}{r}\]
Simplify \(\frac{\frac{240+{9}^{x}}{De{e}^{2}}}{r}\) to \(\frac{240+{9}^{x}}{De{e}^{2}r}\).
\[tmn{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{240+{9}^{x}}{De{e}^{2}r}\]
Divide both sides by \(m\).
\[tn{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{\frac{240+{9}^{x}}{De{e}^{2}r}}{m}\]
Simplify \(\frac{\frac{240+{9}^{x}}{De{e}^{2}r}}{m}\) to \(\frac{240+{9}^{x}}{De{e}^{2}rm}\).
\[tn{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{240+{9}^{x}}{De{e}^{2}rm}\]
Divide both sides by \(n\).
\[t{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{\frac{240+{9}^{x}}{De{e}^{2}rm}}{n}\]
Simplify \(\frac{\frac{240+{9}^{x}}{De{e}^{2}rm}}{n}\) to \(\frac{240+{9}^{x}}{De{e}^{2}rmn}\).
\[t{x}^{x}f\times {8}^{x}\times {9}^{x+2}=-\frac{240+{9}^{x}}{De{e}^{2}rmn}\]
Divide both sides by \({x}^{x}\).
\[tf\times {8}^{x}\times {9}^{x+2}=-\frac{\frac{240+{9}^{x}}{De{e}^{2}rmn}}{{x}^{x}}\]
Simplify \(\frac{\frac{240+{9}^{x}}{De{e}^{2}rmn}}{{x}^{x}}\) to \(\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}}\).
\[tf\times {8}^{x}\times {9}^{x+2}=-\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}}\]
Divide both sides by \(f\).
\[t\times {8}^{x}\times {9}^{x+2}=-\frac{\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}}}{f}\]
Simplify \(\frac{\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}}}{f}\) to \(\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f}\).
\[t\times {8}^{x}\times {9}^{x+2}=-\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f}\]
Divide both sides by \({8}^{x}\).
\[t\times {9}^{x+2}=-\frac{\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f}}{{8}^{x}}\]
Simplify \(\frac{\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f}}{{8}^{x}}\) to \(\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f\times {8}^{x}}\).
\[t\times {9}^{x+2}=-\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f\times {8}^{x}}\]
Divide both sides by \({9}^{x+2}\).
\[t=-\frac{\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f\times {8}^{x}}}{{9}^{x+2}}\]
Simplify \(\frac{\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f\times {8}^{x}}}{{9}^{x+2}}\) to \(\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f\times {8}^{x}\times {9}^{x+2}}\).
\[t=-\frac{240+{9}^{x}}{De{e}^{2}rmn{x}^{x}f\times {8}^{x}\times {9}^{x+2}}\]
t=-(240+9^x)/(De*e^2*r*m*n*x^x*f*8^x*9^(x+2))
