Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{a}^{3}{({b}^{2})}^{3}{c}^{3}}{{a}^{-1}{b}^{4}{c}^{3}}\times \frac{{(a-2{b}^{3}{c}^{5})}^{0}}{{a}^{-1}{b}^{4}{c}^{2}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{a}^{3}{b}^{6}{c}^{3}}{{a}^{-1}{b}^{4}{c}^{3}}\times \frac{{(a-2{b}^{3}{c}^{5})}^{0}}{{a}^{-1}{b}^{4}{c}^{2}}\]
Use Rule of Zero: \({x}^{0}=1\).
\[\frac{{a}^{3}{b}^{6}{c}^{3}}{{a}^{-1}{b}^{4}{c}^{3}}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{2}}\]
Cancel \({c}^{3}\).
\[\frac{{a}^{3}{b}^{6}}{{a}^{-1}{b}^{4}}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{2}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{a}^{3+1}{b}^{6-4}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{2}}\]
Simplify \(3+1\) to \(4\).
\[{a}^{4}{b}^{6-4}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{2}}\]
Simplify \(6-4\) to \(2\).
\[{a}^{4}{b}^{2}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{2}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{{a}^{4}{b}^{2}\times 1}{{a}^{-1}{b}^{4}{c}^{2}}\]
Simplify \({a}^{4}{b}^{2}\times 1\) to \({a}^{4}{b}^{2}\).
\[\frac{{a}^{4}{b}^{2}}{{a}^{-1}{b}^{4}{c}^{2}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{a}^{4+1}{b}^{2-4}{c}^{-2}\]
Simplify \(4+1\) to \(5\).
\[{a}^{5}{b}^{2-4}{c}^{-2}\]
Simplify \(2-4\) to \(-2\).
\[{a}^{5}{b}^{-2}{c}^{-2}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[{a}^{5}\times \frac{1}{{b}^{2}}{c}^{-2}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[{a}^{5}\times \frac{1}{{b}^{2}}\times \frac{1}{{c}^{2}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{{a}^{5}\times 1\times 1}{{b}^{2}{c}^{2}}\]
Simplify \({a}^{5}\times 1\times 1\) to \({a}^{5}\).
\[\frac{{a}^{5}}{{b}^{2}{c}^{2}}\]
a^5/(b^2*c^2)
