Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{\frac{1}{4}}-a^{\frac{9}{4}}}{\frac{1}{4}}-a^{\frac{5}{4}}-\frac{b^{-\frac{1}{2}}-b^{\frac{3}{2}}}{b^{\frac{1}{2}}-b^{\frac{-1}{2}};$$

Answer

$$14-a^9414-a^54-b^-12-b^44-b^-12;$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\begin{aligned}&14-{a}^{9414}-{a}^{54}-{b}^{-12}-{b}^{32+12}-{b}^{-12}\\&\end{aligned}\]
Simplify  \(32+12\)  to  \(44\).
\[\begin{aligned}&14-{a}^{9414}-{a}^{54}-{b}^{-12}-{b}^{44}-{b}^{-12}\\&\end{aligned}\]
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