Question

$$\frac { x ^ { 2 } ( b - c ) } { x ^ { 2 } ( a - c ) } \div ( \frac { x ^ { b } } { x ^ { a } } ) ^ { c } = 1$$

Answer

$$o=1/(Sh*w*t^2*h*a*x^(a+b-(a+b)*c)*(b-c)*(a-c))$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[Showthat{x}^{a}(b-c){x}^{b}\times \frac{a-c}{{({x}^{b+a})}^{c}}=1\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[Showthat{x}^{a}(b-c){x}^{b}\times \frac{a-c}{{x}^{(b+a)c}}=1\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{Showthat{x}^{a}(b-c){x}^{b}(a-c)}{{x}^{(b+a)c}}=1\]
Regroup terms.
\[\frac{owttha{x}^{a}{x}^{b}Sh(b-c)(a-c)}{{x}^{(b+a)c}}=1\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{ow{t}^{1+1}ha{x}^{a+b}Sh(b-c)(a-c)}{{x}^{(b+a)c}}=1\]
Simplify  \(1+1\)  to  \(2\).
\[\frac{ow{t}^{2}ha{x}^{a+b}Sh(b-c)(a-c)}{{x}^{(b+a)c}}=1\]
Regroup terms.
\[\frac{Show{t}^{2}ha{x}^{a+b}(b-c)(a-c)}{{x}^{(b+a)c}}=1\]
Simplify  \(\frac{Show{t}^{2}ha{x}^{a+b}(b-c)(a-c)}{{x}^{(b+a)c}}\)  to  \(\frac{Show{t}^{2}ha{x}^{a+b}(b-c)(a-c)}{{x}^{(a+b)c}}\).
\[\frac{Show{t}^{2}ha{x}^{a+b}(b-c)(a-c)}{{x}^{(a+b)c}}=1\]
Simplify  \(\frac{Show{t}^{2}ha{x}^{a+b}(b-c)(a-c)}{{x}^{(a+b)c}}\)  to  \(Show{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)(a-c)\).
\[Show{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)(a-c)=1\]
Divide both sides by \(Sh\).
\[ow{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{1}{Sh}\]
Divide both sides by \(w\).
\[o{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{\frac{1}{Sh}}{w}\]
Simplify  \(\frac{\frac{1}{Sh}}{w}\)  to  \(\frac{1}{Shw}\).
\[o{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{1}{Shw}\]
Divide both sides by \({t}^{2}\).
\[oha{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{\frac{1}{Shw}}{{t}^{2}}\]
Simplify  \(\frac{\frac{1}{Shw}}{{t}^{2}}\)  to  \(\frac{1}{Shw{t}^{2}}\).
\[oha{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{1}{Shw{t}^{2}}\]
Divide both sides by \(h\).
\[oa{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{\frac{1}{Shw{t}^{2}}}{h}\]
Simplify  \(\frac{\frac{1}{Shw{t}^{2}}}{h}\)  to  \(\frac{1}{Shw{t}^{2}h}\).
\[oa{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{1}{Shw{t}^{2}h}\]
Divide both sides by \(a\).
\[o{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{\frac{1}{Shw{t}^{2}h}}{a}\]
Simplify  \(\frac{\frac{1}{Shw{t}^{2}h}}{a}\)  to  \(\frac{1}{Shw{t}^{2}ha}\).
\[o{x}^{a+b-(a+b)c}(b-c)(a-c)=\frac{1}{Shw{t}^{2}ha}\]
Divide both sides by \({x}^{a+b-(a+b)c}\).
\[o(b-c)(a-c)=\frac{\frac{1}{Shw{t}^{2}ha}}{{x}^{a+b-(a+b)c}}\]
Simplify  \(\frac{\frac{1}{Shw{t}^{2}ha}}{{x}^{a+b-(a+b)c}}\)  to  \(\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}}\).
\[o(b-c)(a-c)=\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}}\]
Divide both sides by \(b-c\).
\[o(a-c)=\frac{\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}}}{b-c}\]
Simplify  \(\frac{\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}}}{b-c}\)  to  \(\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)}\).
\[o(a-c)=\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)}\]
Divide both sides by \(a-c\).
\[o=\frac{\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)}}{a-c}\]
Simplify  \(\frac{\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)}}{a-c}\)  to  \(\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)(a-c)}\).
\[o=\frac{1}{Shw{t}^{2}ha{x}^{a+b-(a+b)c}(b-c)(a-c)}\]