Example

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

Question

$$x^{29-t}; \frac{x^{9}y^{29}\div(x^{2}y)^{9}}{x^{27}-1}\frac{x^{3+9}y^{-1}}$$

Answer

$$x^(29-t);x^9*y^20*x^-18*x^27-x^3+9*y^-1$$

Solution


Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\begin{aligned}&{x}^{29-t}\\&{x}^{9}\times \frac{{y}^{29}}{{({x}^{2})}^{9}{y}^{9}}{x}^{27}-1\times {x}^{3}+9{y}^{-1}\end{aligned}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\begin{aligned}&{x}^{29-t}\\&{x}^{9}\times \frac{{y}^{29}}{{x}^{18}{y}^{9}}{x}^{27}-1\times {x}^{3}+9{y}^{-1}\end{aligned}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[\begin{aligned}&{x}^{29-t}\\&{x}^{9}{y}^{29-9}{x}^{-18}{x}^{27}-1\times {x}^{3}+9{y}^{-1}\end{aligned}\]
Simplify  \(29-9\)  to  \(20\).
\[\begin{aligned}&{x}^{29-t}\\&{x}^{9}{y}^{20}{x}^{-18}{x}^{27}-1\times {x}^{3}+9{y}^{-1}\end{aligned}\]
Simplify  \(1\times {x}^{3}\)  to  \({x}^{3}\).
\[\begin{aligned}&{x}^{29-t}\\&{x}^{9}{y}^{20}{x}^{-18}{x}^{27}-{x}^{3}+9{y}^{-1}\end{aligned}\]
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