Example

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

Question

$$[\frac{(x^{3}y^{5})^{2}}{x^{5}y^{2}}]^{-1}(x^{-3}y^{0})^{2}$$

Answer

$$[(x^3*y^5)^2/(x^11*y^(1/2]))$$

Solution


Use Rule of Zero: \({x}^{0}=1\).
\(\frac{{({x}^{3}{y}^{5})}^{2}}{{x}^{5}{y}^{2}}\)^-1*(x^-3*1)^2
Simplify  \({x}^{-3}\times 1\)  to  \({x}^{-3}\).
\(\frac{{({x}^{3}{y}^{5})}^{2}}{{x}^{5}{y}^{2}}\)^-1*(x^-3)^2
Remove parentheses.
\({({x}^{3}{y}^{5})}^{2}/\)^-1)*(x^-3)^2
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\({({x}^{3}{y}^{5})}^{2}/\)))*(x^-3)^2
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\({({x}^{3}{y}^{5})}^{2}/\)))*x^-6
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
(\({({x}^{3}{y}^{5})}^{2}{x}^{-6}\)))
Regroup terms.
(x^-6*\({({x}^{3}{y}^{5})}^{2}\)))
Simplify.
\({({x}^{3}{y}^{5})}^{2}/\)))
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