$$\left. \begin{array} { l } { \int _ { 0 } ^ { 4 } 4 x e ^ { 4 } d x = d x } \\ { \begin{array} { l } { d } \\ { a ) } \\ { a } \end{array} } \\ { b } \\ { c _ { 0 } } \\ { d } \end{array} \right.$$
Answer
$$f=(a^2*b*c)/(210*g*z*x^2)$$
Solution
Cancel \(d\) on both sides.
\[f\times 4410gzxx=a\times 21abc\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[f\times 4410gz{x}^{2}=a\times 21abc\]
Regroup terms.
\[4410fgz{x}^{2}=a\times 21abc\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[4410fgz{x}^{2}={a}^{2}\times 21bc\]
Regroup terms.
\[4410fgz{x}^{2}=21{a}^{2}bc\]
Divide both sides by \(4410\).
\[fgz{x}^{2}=\frac{21{a}^{2}bc}{4410}\]
Simplify \(\frac{21{a}^{2}bc}{4410}\) to \(\frac{{a}^{2}bc}{210}\).
\[fgz{x}^{2}=\frac{{a}^{2}bc}{210}\]
Divide both sides by \(g\).
\[fz{x}^{2}=\frac{\frac{{a}^{2}bc}{210}}{g}\]
Simplify \(\frac{\frac{{a}^{2}bc}{210}}{g}\) to \(\frac{{a}^{2}bc}{210g}\).
\[fz{x}^{2}=\frac{{a}^{2}bc}{210g}\]
Divide both sides by \(z\).
\[f{x}^{2}=\frac{\frac{{a}^{2}bc}{210g}}{z}\]
Simplify \(\frac{\frac{{a}^{2}bc}{210g}}{z}\) to \(\frac{{a}^{2}bc}{210gz}\).
\[f{x}^{2}=\frac{{a}^{2}bc}{210gz}\]
Divide both sides by \({x}^{2}\).
\[f=\frac{\frac{{a}^{2}bc}{210gz}}{{x}^{2}}\]
Simplify \(\frac{\frac{{a}^{2}bc}{210gz}}{{x}^{2}}\) to \(\frac{{a}^{2}bc}{210gz{x}^{2}}\).
