Cancel \(r\) on both sides.
\[at\imath oof\times 80pa\imath seto\times 3rs=thefact\imath on\imath n\]
Take out the constants.
\[(80\times 3)aattooofpssr\imath \imath e=thefact\imath on\imath n\]
Simplify \(80\times 3\) to \(240\).
\[240aattooofpssr\imath \imath e=thefact\imath on\imath n\]
Simplify \(240aattooofpssr\imath \imath e\) to \(240{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r\imath \imath e\).
\[240{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r\imath \imath e=thefact\imath on\imath n\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[240{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r{\imath }^{2}e=thefact\imath on\imath n\]
Use Square Rule: \({i}^{2}=-1\).
\[240{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r\times -1\times e=thefact\imath on\imath n\]
Simplify \(240{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r\times -1\times e\) to \(-240{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}re\).
\[-240{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}re=thefact\imath on\imath n\]
Regroup terms.
\[-240e{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r=thefact\imath on\imath n\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[-240e{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r={t}^{2}hefac{\imath }^{2}o{n}^{2}\]
Use Square Rule: \({i}^{2}=-1\).
\[-240e{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r={t}^{2}hefac\times -1\times o{n}^{2}\]
Simplify \({t}^{2}hefac\times -1\times o{n}^{2}\) to \({t}^{2}hefac\times -o{n}^{2}\).
\[-240e{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r={t}^{2}hefac\times -o{n}^{2}\]
Regroup terms.
\[-240e{a}^{2}{t}^{2}{o}^{3}fp{s}^{2}r=-e{t}^{2}hfaco{n}^{2}\]
Cancel \({t}^{2}\) on both sides.
\[-240e{a}^{2}{o}^{3}fp{s}^{2}r=-ehfaco{n}^{2}\]
Cancel \(f\) on both sides.
\[-240e{a}^{2}{o}^{3}p{s}^{2}r=-ehaco{n}^{2}\]
Divide both sides by \(-240\).
\[e{a}^{2}{o}^{3}p{s}^{2}r=\frac{-ehaco{n}^{2}}{-240}\]
Two negatives make a positive.
\[e{a}^{2}{o}^{3}p{s}^{2}r=\frac{ehaco{n}^{2}}{240}\]
Divide both sides by \(e\).
\[{a}^{2}{o}^{3}p{s}^{2}r=\frac{\frac{ehaco{n}^{2}}{240}}{e}\]
Simplify \(\frac{\frac{ehaco{n}^{2}}{240}}{e}\) to \(\frac{ehaco{n}^{2}}{240e}\).
\[{a}^{2}{o}^{3}p{s}^{2}r=\frac{ehaco{n}^{2}}{240e}\]
Cancel \(e\).
\[{a}^{2}{o}^{3}p{s}^{2}r=\frac{haco{n}^{2}}{240}\]
Divide both sides by \({a}^{2}\).
\[{o}^{3}p{s}^{2}r=\frac{\frac{haco{n}^{2}}{240}}{{a}^{2}}\]
Simplify \(\frac{\frac{haco{n}^{2}}{240}}{{a}^{2}}\) to \(\frac{haco{n}^{2}}{240{a}^{2}}\).
\[{o}^{3}p{s}^{2}r=\frac{haco{n}^{2}}{240{a}^{2}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{o}^{3}p{s}^{2}r=\frac{h{a}^{1-2}co{n}^{2}}{240}\]
Simplify \(1-2\) to \(-1\).
\[{o}^{3}p{s}^{2}r=\frac{h{a}^{-1}co{n}^{2}}{240}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[{o}^{3}p{s}^{2}r=\frac{h\times \frac{1}{a}co{n}^{2}}{240}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[{o}^{3}p{s}^{2}r=\frac{\frac{h\times 1\times co{n}^{2}}{a}}{240}\]
Simplify \(h\times 1\times co{n}^{2}\) to \(hco{n}^{2}\).
\[{o}^{3}p{s}^{2}r=\frac{\frac{hco{n}^{2}}{a}}{240}\]
Simplify \(\frac{\frac{hco{n}^{2}}{a}}{240}\) to \(\frac{hco{n}^{2}}{240a}\).
\[{o}^{3}p{s}^{2}r=\frac{hco{n}^{2}}{240a}\]
Divide both sides by \({o}^{3}\).
\[p{s}^{2}r=\frac{\frac{hco{n}^{2}}{240a}}{{o}^{3}}\]
Simplify \(\frac{\frac{hco{n}^{2}}{240a}}{{o}^{3}}\) to \(\frac{hco{n}^{2}}{240a{o}^{3}}\).
\[p{s}^{2}r=\frac{hco{n}^{2}}{240a{o}^{3}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[p{s}^{2}r=\frac{hc{o}^{1-3}{n}^{2}{a}^{-1}}{240}\]
Simplify \(1-3\) to \(-2\).
\[p{s}^{2}r=\frac{hc{o}^{-2}{n}^{2}{a}^{-1}}{240}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[p{s}^{2}r=\frac{hc\times \frac{1}{{o}^{2}}{n}^{2}{a}^{-1}}{240}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[p{s}^{2}r=\frac{hc\times \frac{1}{{o}^{2}}{n}^{2}\times \frac{1}{a}}{240}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[p{s}^{2}r=\frac{\frac{hc\times 1\times {n}^{2}\times 1}{{o}^{2}a}}{240}\]
Simplify \(hc\times 1\times {n}^{2}\times 1\) to \(hc{n}^{2}\).
\[p{s}^{2}r=\frac{\frac{hc{n}^{2}}{{o}^{2}a}}{240}\]
Simplify \(\frac{\frac{hc{n}^{2}}{{o}^{2}a}}{240}\) to \(\frac{hc{n}^{2}}{240{o}^{2}a}\).
\[p{s}^{2}r=\frac{hc{n}^{2}}{240{o}^{2}a}\]
Divide both sides by \({s}^{2}\).
\[pr=\frac{\frac{hc{n}^{2}}{240{o}^{2}a}}{{s}^{2}}\]
Simplify \(\frac{\frac{hc{n}^{2}}{240{o}^{2}a}}{{s}^{2}}\) to \(\frac{hc{n}^{2}}{240{o}^{2}a{s}^{2}}\).
\[pr=\frac{hc{n}^{2}}{240{o}^{2}a{s}^{2}}\]
Divide both sides by \(r\).
\[p=\frac{\frac{hc{n}^{2}}{240{o}^{2}a{s}^{2}}}{r}\]
Simplify \(\frac{\frac{hc{n}^{2}}{240{o}^{2}a{s}^{2}}}{r}\) to \(\frac{hc{n}^{2}}{240{o}^{2}a{s}^{2}r}\).
\[p=\frac{hc{n}^{2}}{240{o}^{2}a{s}^{2}r}\]
p=(h*c*n^2)/(240*o^2*a*s^2*r)
