Question

$$\left. \begin{array} { l } { \begin{array} { l } { \quad \frac { 2 } { 3 } \times [ ] = \frac { 20 } { 21 } } \end{array} } \end{array} \right.$$

Answer

$$v=-2021/(23*Pr*e^4*Bo*o^2*d*t^2*h^2*n^2*u*m*b^2*r*x)$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[Pr{o}^{2}v{\imath }^{2}d{e}^{4}{t}^{2}{h}^{2}{n}^{2}um{b}^{2}r\times 23Box=2021\]
Use Square Rule: \({i}^{2}=-1\).
\[Pr{o}^{2}v\times -1\times d{e}^{4}{t}^{2}{h}^{2}{n}^{2}um{b}^{2}r\times 23Box=2021\]
Simplify  \(Pr{o}^{2}v\times -1\times d{e}^{4}{t}^{2}{h}^{2}{n}^{2}um{b}^{2}r\times 23Box\)  to  \(-23{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rxPr{e}^{4}Bo\).
\[-23{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rxPr{e}^{4}Bo=2021\]
Regroup terms.
\[-23Pr{e}^{4}Bo{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=2021\]
Divide both sides by \(-23\).
\[Pr{e}^{4}Bo{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{2021}{23}\]
Divide both sides by \(Pr\).
\[{e}^{4}Bo{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{\frac{2021}{23}}{Pr}\]
Simplify  \(\frac{\frac{2021}{23}}{Pr}\)  to  \(\frac{2021}{23Pr}\).
\[{e}^{4}Bo{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{2021}{23Pr}\]
Divide both sides by \({e}^{4}\).
\[Bo{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{\frac{2021}{23Pr}}{{e}^{4}}\]
Simplify  \(\frac{\frac{2021}{23Pr}}{{e}^{4}}\)  to  \(\frac{2021}{23Pr{e}^{4}}\).
\[Bo{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}}\]
Divide both sides by \(Bo\).
\[{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{\frac{2021}{23Pr{e}^{4}}}{Bo}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}}}{Bo}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo}\).
\[{o}^{2}vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}Bo}\]
Divide both sides by \({o}^{2}\).
\[vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{\frac{2021}{23Pr{e}^{4}Bo}}{{o}^{2}}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo}}{{o}^{2}}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}}\).
\[vd{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}}\]
Divide both sides by \(d\).
\[v{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}}}{d}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}}}{d}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d}\).
\[v{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d}\]
Divide both sides by \({t}^{2}\).
\[v{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d}}{{t}^{2}}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d}}{{t}^{2}}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}}\).
\[v{h}^{2}{n}^{2}um{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}}\]
Divide both sides by \({h}^{2}\).
\[v{n}^{2}um{b}^{2}rx=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}}}{{h}^{2}}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}}}{{h}^{2}}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}}\).
\[v{n}^{2}um{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}}\]
Divide both sides by \({n}^{2}\).
\[vum{b}^{2}rx=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}}}{{n}^{2}}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}}}{{n}^{2}}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}}\).
\[vum{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}}\]
Divide both sides by \(u\).
\[vm{b}^{2}rx=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}}}{u}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}}}{u}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}u}\).
\[vm{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}u}\]
Divide both sides by \(m\).
\[v{b}^{2}rx=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}u}}{m}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}u}}{m}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um}\).
\[v{b}^{2}rx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um}\]
Divide both sides by \({b}^{2}\).
\[vrx=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um}}{{b}^{2}}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um}}{{b}^{2}}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}}\).
\[vrx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}}\]
Divide both sides by \(r\).
\[vx=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}}}{r}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}}}{r}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}r}\).
\[vx=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}r}\]
Divide both sides by \(x\).
\[v=-\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}r}}{x}\]
Simplify  \(\frac{\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}r}}{x}\)  to  \(\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx}\).
\[v=-\frac{2021}{23Pr{e}^{4}Bo{o}^{2}d{t}^{2}{h}^{2}{n}^{2}um{b}^{2}rx}\]