Regroup terms.
\[\frac{{(\frac{{a}^{4}{y}^{-2}}{4b{x}^{-1}})}^{-3}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{\frac{1}{{(\frac{{a}^{4}{y}^{-2}}{4b{x}^{-1}})}^{3}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{1}{\frac{{({a}^{4}{y}^{-2})}^{3}}{{(4b{x}^{-1})}^{3}}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{\frac{1}{\frac{{({a}^{4})}^{3}{({y}^{-2})}^{3}}{{(4b{x}^{-1})}^{3}}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{1}{\frac{{a}^{12}{({y}^{-2})}^{3}}{{(4b{x}^{-1})}^{3}}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{1}{\frac{{a}^{12}{y}^{-6}}{{(4b{x}^{-1})}^{3}}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{\frac{1}{\frac{{a}^{12}{y}^{-6}}{{4}^{3}{b}^{3}{({x}^{-1})}^{3}}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Simplify \({4}^{3}\) to \(64\).
\[\frac{\frac{1}{\frac{{a}^{12}{y}^{-6}}{64{b}^{3}{({x}^{-1})}^{3}}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{1}{\frac{{a}^{12}{y}^{-6}}{64{b}^{3}{x}^{-3}}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Invert and multiply.
\[\frac{\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}}{{(\frac{{a}^{-1}{b}^{4}}{{x}^{-3}{y}^{4}})}^{2}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}}{\frac{{({a}^{-1}{b}^{4})}^{2}}{{({x}^{-3}{y}^{4})}^{2}}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}}{\frac{{({a}^{-1})}^{2}{({b}^{4})}^{2}}{{({x}^{-3}{y}^{4})}^{2}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}}{\frac{{a}^{-2}{({b}^{4})}^{2}}{{({x}^{-3}{y}^{4})}^{2}}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}}{\frac{{a}^{-2}{b}^{8}}{{({x}^{-3}{y}^{4})}^{2}}}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}}{\frac{{a}^{-2}{b}^{8}}{{({x}^{-3})}^{2}{({y}^{4})}^{2}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}}{\frac{{a}^{-2}{b}^{8}}{{x}^{-6}{({y}^{4})}^{2}}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}}{\frac{{a}^{-2}{b}^{8}}{{x}^{-6}{y}^{8}}}\]
Invert and multiply.
\[\frac{64{b}^{3}{x}^{-3}}{{a}^{12}{y}^{-6}}\times \frac{{x}^{-6}{y}^{8}}{{a}^{-2}{b}^{8}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{64{b}^{3}{x}^{-3}{x}^{-6}{y}^{8}}{{a}^{12}{y}^{-6}{a}^{-2}{b}^{8}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{64{b}^{3}{x}^{-3-6}{y}^{8}}{{a}^{12}{y}^{-6}{a}^{-2}{b}^{8}}\]
Simplify \(-3-6\) to \(-9\).
\[\frac{64{b}^{3}{x}^{-9}{y}^{8}}{{a}^{12}{y}^{-6}{a}^{-2}{b}^{8}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{64{b}^{3}\times \frac{1}{{x}^{9}}{y}^{8}}{{a}^{12}{y}^{-6}{a}^{-2}{b}^{8}}\]
Simplify \(64{b}^{3}\times \frac{1}{{x}^{9}}{y}^{8}\) to \(\frac{64{b}^{3}{y}^{8}}{{x}^{9}}\).
\[\frac{\frac{64{b}^{3}{y}^{8}}{{x}^{9}}}{{a}^{12}{y}^{-6}{a}^{-2}{b}^{8}}\]
Regroup terms.
\[\frac{\frac{64{b}^{3}{y}^{8}}{{x}^{9}}}{{a}^{12}{a}^{-2}{y}^{-6}{b}^{8}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{\frac{64{b}^{3}{y}^{8}}{{x}^{9}}}{{a}^{12-2}{y}^{-6}{b}^{8}}\]
Simplify \(12-2\) to \(10\).
\[\frac{\frac{64{b}^{3}{y}^{8}}{{x}^{9}}}{{a}^{10}{y}^{-6}{b}^{8}}\]
Simplify.
\[\frac{64{b}^{3}{y}^{8}}{{x}^{9}{a}^{10}{y}^{-6}{b}^{8}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[64{b}^{3-8}{y}^{8+6}{x}^{-9}{a}^{-10}\]
Simplify \(3-8\) to \(-5\).
\[64{b}^{-5}{y}^{8+6}{x}^{-9}{a}^{-10}\]
Simplify \(8+6\) to \(14\).
\[64{b}^{-5}{y}^{14}{x}^{-9}{a}^{-10}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[64\times \frac{1}{{b}^{5}}{y}^{14}{x}^{-9}{a}^{-10}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[64\times \frac{1}{{b}^{5}}{y}^{14}\times \frac{1}{{x}^{9}}{a}^{-10}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[64\times \frac{1}{{b}^{5}}{y}^{14}\times \frac{1}{{x}^{9}}\times \frac{1}{{a}^{10}}\]
Simplify.
\[\frac{64{y}^{14}}{{b}^{5}{x}^{9}{a}^{10}}\]
(64*y^14)/(b^5*x^9*a^10)
