Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{10}^{8}{({5}^{3})}^{4}}{{({5}^{4})}^{3}{({10}^{2})}^{5}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Simplify \({10}^{8}\) to \(100000000\).
\[\frac{100000000{({5}^{3})}^{4}}{{({5}^{4})}^{3}{({10}^{2})}^{5}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{100000000\times {5}^{12}}{{({5}^{4})}^{3}{({10}^{2})}^{5}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Simplify \({5}^{12}\) to \(244140625\).
\[\frac{100000000\times 244140625}{{({5}^{4})}^{3}{({10}^{2})}^{5}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Simplify \(100000000\times 244140625\) to \(2.441406\times {10}^{16}\).
\[\frac{2.441406\times {10}^{16}}{{({5}^{4})}^{3}{({10}^{2})}^{5}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Simplify \(2.441406\times {10}^{16}\) to \((2.441406)\times {10}^{16}\).
\[\frac{2.441406\times {10}^{16}}{{({5}^{4})}^{3}{({10}^{2})}^{5}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{2.441406\times {10}^{16}}{{5}^{12}{({10}^{2})}^{5}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Simplify \({5}^{12}\) to \(244140625\).
\[\frac{2.441406\times {10}^{16}}{244140625{({10}^{2})}^{5}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{2.441406\times {10}^{16}}{244140625\times {10}^{10}}\times \frac{{({10}^{5})}^{3}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{2.441406\times {10}^{16}}{244140625\times {10}^{10}}\times \frac{{10}^{15}{({2}^{4})}^{3}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{2.441406\times {10}^{16}}{244140625\times {10}^{10}}\times \frac{{10}^{15}\times {2}^{12}}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Simplify \({2}^{12}\) to \(4096\).
\[\frac{2.441406\times {10}^{16}}{244140625\times {10}^{10}}\times \frac{{10}^{15}\times 4096}{{({2}^{2})}^{4}{({10}^{2})}^{6}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{2.441406\times {10}^{16}}{244140625\times {10}^{10}}\times \frac{{10}^{15}\times 4096}{{2}^{8}{({10}^{2})}^{6}}\]
Simplify \({2}^{8}\) to \(256\).
\[\frac{2.441406\times {10}^{16}}{244140625\times {10}^{10}}\times \frac{{10}^{15}\times 4096}{256{({10}^{2})}^{6}}\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{2.441406\times {10}^{16}}{244140625\times {10}^{10}}\times \frac{{10}^{15}\times 4096}{256\times {10}^{12}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[2.441406\times {10}^{16-10}\times {244140625}^{-1}\times \frac{{10}^{15}\times 4096}{256\times {10}^{12}}\]
Simplify \(16-10\) to \(6\).
\[2.441406\times {10}^{6}\times {244140625}^{-1}\times \frac{{10}^{15}\times 4096}{256\times {10}^{12}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[2.441406\times {10}^{6}\times \frac{1}{244140625}\times \frac{{10}^{15}\times 4096}{256\times {10}^{12}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{2.441406\times {10}^{6}\times 1\times {10}^{15}\times 4096}{244140625\times 256\times {10}^{12}}\]
Simplify \(2.441406\times {10}^{6}\times 1\times {10}^{15}\times 4096\) to \(10000\times {10}^{6}\times {10}^{15}\).
\[\frac{10000\times {10}^{6}\times {10}^{15}}{244140625\times 256\times {10}^{12}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{10000\times {10}^{21}}{244140625\times 256\times {10}^{12}}\]
Simplify \(244140625\times 256\) to \(62500000000\).
\[\frac{10000\times {10}^{21}}{62500000000\times {10}^{12}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[10000\times {10}^{21-12}\times {62500000000}^{-1}\]
Simplify \(21-12\) to \(9\).
\[10000\times {10}^{9}\times {62500000000}^{-1}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[10000\times {10}^{9}\times \frac{1}{62500000000}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{10000\times {10}^{9}\times 1}{62500000000}\]
Simplify \(10000\times {10}^{9}\times 1\) to \(10000\times {10}^{9}\).
\[\frac{10000\times {10}^{9}}{62500000000}\]
(10000*10^9)/62500000000
