Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\begin{aligned}&1\times fx={3}^{13}+\frac{1}{{3}^{13}}\\&showthat\times 3{x}^{3}-9x=10\end{aligned}\]
Simplify \(1\times fx\) to \(fx\).
\[\begin{aligned}&fx={3}^{13}+\frac{1}{{3}^{13}}\\&showthat\times 3{x}^{3}-9x=10\end{aligned}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\begin{aligned}&fx={3}^{13}+\frac{1}{{3}^{13}}\\&s{h}^{2}ow{t}^{2}a\times 3{x}^{3}-9x=10\end{aligned}\]
Regroup terms.
\[\begin{aligned}&fx={3}^{13}+\frac{1}{{3}^{13}}\\&3s{h}^{2}ow{t}^{2}a{x}^{3}-9x=10\end{aligned}\]
Break down the problem into these 2 equations.
\[fx={3}^{13}+\frac{1}{{3}^{13}}\]
\[fx=3s{h}^{2}ow{t}^{2}a{x}^{3}-9x\]
Solve the 1st equation: \(fx={3}^{13}+\frac{1}{{3}^{13}}\).
Divide both sides by \(f\).
\[x=\frac{{3}^{13}+\frac{1}{{3}^{13}}}{f}\]
\[x=\frac{{3}^{13}+\frac{1}{{3}^{13}}}{f}\]
Solve the 2nd equation: \(fx=3s{h}^{2}ow{t}^{2}a{x}^{3}-9x\).
Move all terms to one side.
\[fx-3s{h}^{2}ow{t}^{2}a{x}^{3}+9x=0\]
Factor out the common term \(x\).
\[x(f-3s{h}^{2}ow{t}^{2}a{x}^{2}+9)=0\]
Solve for \(x\).
Ask: When will \(x(f-3s{h}^{2}ow{t}^{2}a{x}^{2}+9)\) equal zero?
When \(x=0\) or \(f-3s{h}^{2}ow{t}^{2}a{x}^{2}+9=0\)
Solve each of the 2 equations above.
\[x=0,\pm \sqrt{\frac{\frac{f}{3}+3}{s{h}^{2}ow{t}^{2}a}}\]
\[x=0,\pm \sqrt{\frac{\frac{f}{3}+3}{s{h}^{2}ow{t}^{2}a}}\]
\[x=0,\pm \sqrt{\frac{\frac{f}{3}+3}{s{h}^{2}ow{t}^{2}a}}\]
Collect all solutions.
\[x=\frac{{3}^{13}+\frac{1}{{3}^{13}}}{f},0,\pm \sqrt{\frac{\frac{f}{3}+3}{s{h}^{2}ow{t}^{2}a}}\]
x=(3^13+1/3^13)/f,0,sqrt((f/3+3)/(s*h^2*o*w*t^2*a)),-sqrt((f/3+3)/(s*h^2*o*w*t^2*a))
