Since the power of 17 is odd, the result will be negative.
\[\frac{-{(\frac{11}{2})}^{17}}{{(-\frac{11}{2})}^{25}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{-\frac{{11}^{17}}{{2}^{17}}}{{(-\frac{11}{2})}^{25}}\]
Simplify \({11}^{17}\) to \(5.054470\times {10}^{17}\).
\[\frac{-\frac{5.054470\times {10}^{17}}{{2}^{17}}}{{(-\frac{11}{2})}^{25}}\]
Simplify \({2}^{17}\) to \(131072\).
\[\frac{-\frac{5.054470\times {10}^{17}}{131072}}{{(-\frac{11}{2})}^{25}}\]
Since the power of 25 is odd, the result will be negative.
\[\frac{-\frac{5.054470\times {10}^{17}}{131072}}{-{(\frac{11}{2})}^{25}}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{-\frac{5.054470\times {10}^{17}}{131072}}{-\frac{{11}^{25}}{{2}^{25}}}\]
Simplify \({11}^{25}\) to \(1.083471\times {10}^{26}\).
\[\frac{-\frac{5.054470\times {10}^{17}}{131072}}{-\frac{1.083471\times {10}^{26}}{{2}^{25}}}\]
Simplify \({2}^{25}\) to \(33554432\).
\[\frac{-\frac{5.054470\times {10}^{17}}{131072}}{-\frac{1.083471\times {10}^{26}}{33554432}}\]
Two negatives make a positive.
\[\frac{\frac{5.054470\times {10}^{17}}{131072}}{\frac{1.083471\times {10}^{26}}{33554432}}\]
Invert and multiply.
\[\frac{5.054470\times {10}^{17}}{131072}\times \frac{33554432}{1.083471\times {10}^{26}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{5.054470\times {10}^{17}\times 33554432}{131072\times 1.083471\times {10}^{26}}\]
Simplify \(5.054470\times {10}^{17}\times 33554432\) to \((169599879.47381)\times {10}^{17}\).
\[\frac{169599879.47381\times {10}^{17}}{131072\times 1.083471\times {10}^{26}}\]
Simplify \(131072\times 1.083471\) to \(142012.657741\).
\[\frac{169599879.47381\times {10}^{17}}{142012.657741\times {10}^{26}}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[169599879.47381\times {10}^{17-26}\times {142012.657741}^{-1}\]
Simplify \(17-26\) to \(-9\).
\[169599879.47381\times {10}^{-9}\times {142012.657741}^{-1}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[169599879.47381\times {10}^{-9}\times \frac{1}{142012.657741}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{169599879.47381\times {10}^{-9}\times 1}{142012.657741}\]
Simplify \(169599879.47381\times {10}^{-9}\times 1\) to \((169599879.47381)\times {10}^{-9}\).
\[\frac{169599879.47381\times {10}^{-9}}{142012.657741}\]
(169599879.47381*10^-9)/142012.65774118
