Question

$$m 9 ^ { m } \div 3 ^ { - 2 } = 9 ^ { 4 }$$

Answer

$$v=9^4.-(m+1)/(e*IM*a*l*u*o^2*f^2*m*r*w*h^2*c)$$

Solution


Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[valueofmforwh\imath ch\times \frac{{9}^{m}}{\frac{1}{{3}^{2}}}={9}^{4.}\]
Simplify  \({3}^{2}\)  to  \(9\).
\[valueofmforwh\imath ch\times \frac{{9}^{m}}{\frac{1}{9}}={9}^{4.}\]
Invert and multiply.
\[valueofmforwh\imath ch\times {9}^{m}\times 9={9}^{4.}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[value{o}^{2}{f}^{2}mrw{h}^{2}\imath c\times {9}^{m+1}={9}^{4.}\]
Regroup terms.
\[e\imath valu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}={9}^{4.}\]
Divide both sides by \(e\).
\[\imath valu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e}\]
Divide both sides by \(\imath \).
\[valu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e}}{\imath }\]
Simplify  \(\frac{\frac{{9}^{4.}}{e}}{\imath }\)  to  \(\frac{{9}^{4.}}{e\imath }\).
\[valu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath }\]
Divide both sides by \(a\).
\[vlu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath }}{a}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath }}{a}\)  to  \(\frac{{9}^{4.}}{e\imath a}\).
\[vlu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath a}\]
Divide both sides by \(l\).
\[vu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath a}}{l}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath a}}{l}\)  to  \(\frac{{9}^{4.}}{e\imath al}\).
\[vu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath al}\]
Divide both sides by \(u\).
\[v{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath al}}{u}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath al}}{u}\)  to  \(\frac{{9}^{4.}}{e\imath alu}\).
\[v{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath alu}\]
Divide both sides by \({o}^{2}\).
\[v{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath alu}}{{o}^{2}}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath alu}}{{o}^{2}}\)  to  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}}\).
\[v{f}^{2}mrw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath alu{o}^{2}}\]
Divide both sides by \({f}^{2}\).
\[vmrw{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}}}{{f}^{2}}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}}}{{f}^{2}}\)  to  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}}\).
\[vmrw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}}\]
Divide both sides by \(m\).
\[vrw{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}}}{m}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}}}{m}\)  to  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}m}\).
\[vrw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}m}\]
Divide both sides by \(r\).
\[vw{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}m}}{r}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}m}}{r}\)  to  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mr}\).
\[vw{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mr}\]
Divide both sides by \(w\).
\[v{h}^{2}c\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mr}}{w}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mr}}{w}\)  to  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw}\).
\[v{h}^{2}c\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw}\]
Divide both sides by \({h}^{2}\).
\[vc\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw}}{{h}^{2}}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw}}{{h}^{2}}\)  to  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}}\).
\[vc\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}}\]
Divide both sides by \(c\).
\[v\times {9}^{m+1}=\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}}}{c}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}}}{c}\)  to  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c}\).
\[v\times {9}^{m+1}=\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c}\]
Divide both sides by \({9}^{m+1}\).
\[v=\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c}}{{9}^{m+1}}\]
Simplify  \(\frac{\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c}}{{9}^{m+1}}\)  to  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}}\).
\[v=\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}}\]
Simplify  \(\frac{{9}^{4.}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c\times {9}^{m+1}}\)  to  \(\frac{{9}^{4.-(m+1)}}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c}\).
\[v={9}^{4.}-\frac{m+1}{e\imath alu{o}^{2}{f}^{2}mrw{h}^{2}c}\]