Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{a}^{3}{({b}^{2})}^{3}{c}^{3}}{{a}^{-1}{b}^{7}{c}^{3}}\times \frac{{({a}^{-2}{b}^{7}{c}^{5})}^{0}}{{a}^{-1}{b}^{4}{c}^{3}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{a}^{3}{b}^{6}{c}^{3}}{{a}^{-1}{b}^{7}{c}^{3}}\times \frac{{({a}^{-2}{b}^{7}{c}^{5})}^{0}}{{a}^{-1}{b}^{4}{c}^{3}}\]
Use Rule of Zero: \({x}^{0}=1\).
\[\frac{{a}^{3}{b}^{6}{c}^{3}}{{a}^{-1}{b}^{7}{c}^{3}}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{3}}\]
Cancel \({c}^{3}\).
\[\frac{{a}^{3}{b}^{6}}{{a}^{-1}{b}^{7}}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{3}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{a}^{3+1}{b}^{6-7}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{3}}\]
Simplify \(3+1\) to \(4\).
\[{a}^{4}{b}^{6-7}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{3}}\]
Simplify \(6-7\) to \(-1\).
\[{a}^{4}{b}^{-1}\times \frac{1}{{a}^{-1}{b}^{4}{c}^{3}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{{a}^{4}{b}^{-1}\times 1}{{a}^{-1}{b}^{4}{c}^{3}}\]
Simplify \({a}^{4}{b}^{-1}\times 1\) to \({a}^{4}{b}^{-1}\).
\[\frac{{a}^{4}{b}^{-1}}{{a}^{-1}{b}^{4}{c}^{3}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[{a}^{4+1}{b}^{-1-4}{c}^{-3}\]
Simplify \(4+1\) to \(5\).
\[{a}^{5}{b}^{-1-4}{c}^{-3}\]
Simplify \(-1-4\) to \(-5\).
\[{a}^{5}{b}^{-5}{c}^{-3}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[{a}^{5}\times \frac{1}{{b}^{5}}{c}^{-3}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[{a}^{5}\times \frac{1}{{b}^{5}}\times \frac{1}{{c}^{3}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{{a}^{5}\times 1\times 1}{{b}^{5}{c}^{3}}\]
Simplify \({a}^{5}\times 1\times 1\) to \({a}^{5}\).
\[\frac{{a}^{5}}{{b}^{5}{c}^{3}}\]
a^5/(b^5*c^3)
