Question

$$p ^ { 2 } \times q ^ { \prime } \times r ^ { 4 } \times s ^ { 3 } = 315000$$

Answer

$$p=sqrt((315000*e*t*h*n)/(q*r^4*s^3)),-sqrt((315000*e*t*h*n)/(q*r^4*s^3))$$

Solution


Use Rule of One: \({x}^{1}=x\).
\[{p}^{2}q{r}^{4}{s}^{3}=315000then\]
Regroup terms.
\[{p}^{2}q{r}^{4}{s}^{3}=315000ethn\]
Divide both sides by \(q\).
\[{p}^{2}{r}^{4}{s}^{3}=\frac{315000ethn}{q}\]
Divide both sides by \({r}^{4}\).
\[{p}^{2}{s}^{3}=\frac{\frac{315000ethn}{q}}{{r}^{4}}\]
Simplify  \(\frac{\frac{315000ethn}{q}}{{r}^{4}}\)  to  \(\frac{315000ethn}{q{r}^{4}}\).
\[{p}^{2}{s}^{3}=\frac{315000ethn}{q{r}^{4}}\]
Divide both sides by \({s}^{3}\).
\[{p}^{2}=\frac{\frac{315000ethn}{q{r}^{4}}}{{s}^{3}}\]
Simplify  \(\frac{\frac{315000ethn}{q{r}^{4}}}{{s}^{3}}\)  to  \(\frac{315000ethn}{q{r}^{4}{s}^{3}}\).
\[{p}^{2}=\frac{315000ethn}{q{r}^{4}{s}^{3}}\]
Take the square root of both sides.
\[p=\pm \sqrt{\frac{315000ethn}{q{r}^{4}{s}^{3}}}\]