Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{a}^{2}{b}^{2}{x}^{4}\times {6}^{24}{a}^{24}{({b}^{-2})}^{24}a{b}^{2}x\times 12{a}^{9}{b}^{7}\]
Simplify \({6}^{24}\) to \(4.738381\times {10}^{18}\).
\[{a}^{2}{b}^{2}{x}^{4}\times 4.738381\times {10}^{18}{a}^{24}{({b}^{-2})}^{24}a{b}^{2}x\times 12{a}^{9}{b}^{7}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[{a}^{2}{b}^{2}{x}^{4}\times 4.738381\times {10}^{18}{a}^{24}{b}^{-48}a{b}^{2}x\times 12{a}^{9}{b}^{7}\]
Take out the constants.
\[(4.738381\times 12){a}^{2}{a}^{24}a{a}^{9}{b}^{2}{b}^{-48}{b}^{2}{b}^{7}{x}^{4}x\times {10}^{18}\]
Simplify \(4.738381\times 12\) to \(56.860576\).
\[56.860576{a}^{2}{a}^{24}a{a}^{9}{b}^{2}{b}^{-48}{b}^{2}{b}^{7}{x}^{4}x\times {10}^{18}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[56.860576{a}^{2+24+1+9}{b}^{2-48+2+7}{x}^{4+1}\times {10}^{18}\]
Simplify \(2+24\) to \(26\).
\[56.860576{a}^{26+1+9}{b}^{2-48+2+7}{x}^{4+1}\times {10}^{18}\]
Simplify \(26+1\) to \(27\).
\[56.860576{a}^{27+9}{b}^{2-48+2+7}{x}^{4+1}\times {10}^{18}\]
Simplify \(27+9\) to \(36\).
\[56.860576{a}^{36}{b}^{2-48+2+7}{x}^{4+1}\times {10}^{18}\]
Simplify \(2-48\) to \(-46\).
\[56.860576{a}^{36}{b}^{-46+2+7}{x}^{4+1}\times {10}^{18}\]
Simplify \(-46+2\) to \(-44\).
\[56.860576{a}^{36}{b}^{-44+7}{x}^{4+1}\times {10}^{18}\]
Simplify \(-44+7\) to \(-37\).
\[56.860576{a}^{36}{b}^{-37}{x}^{4+1}\times {10}^{18}\]
Simplify \(4+1\) to \(5\).
\[56.860576{a}^{36}{b}^{-37}{x}^{5}\times {10}^{18}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[56.860576{a}^{36}\times \frac{1}{{b}^{37}}{x}^{5}\times {10}^{18}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{56.860576{a}^{36}\times 1\times {x}^{5}\times {10}^{18}}{{b}^{37}}\]
Simplify \(56.860576{a}^{36}\times 1\times {x}^{5}\times {10}^{18}\) to \((56.860576){a}^{36}{x}^{5}\times {10}^{18}\).
\[\frac{56.860576{a}^{36}{x}^{5}\times {10}^{18}}{{b}^{37}}\]
Regroup terms.
\[\frac{56.860576\times {10}^{18}{a}^{36}{x}^{5}}{{b}^{37}}\]
(56.860576059859*10^18*a^36*x^5)/b^37
