Evaluate
\frac{289}{40}=7.225
Factor
\frac{17 ^ {2}}{2 ^ {3} \cdot 5} = 7\frac{9}{40} = 7.225
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\left(\frac{\left(2-\frac{3}{9\times 3}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}
Express \frac{\frac{3}{9}}{3} as a single fraction.
\left(\frac{\left(2-\frac{3}{27}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}
Multiply 9 and 3 to get 27.
\left(\frac{\left(2-\frac{1}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}
Reduce the fraction \frac{3}{27} to lowest terms by extracting and canceling out 3.
\left(\frac{\left(\frac{17}{9}\right)^{-2}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}
Subtract \frac{1}{9} from 2 to get \frac{17}{9}.
\left(\frac{\frac{81}{289}}{\left(\frac{9}{4}\right)^{2}\times \frac{2}{5}}\right)^{-1}
Calculate \frac{17}{9} to the power of -2 and get \frac{81}{289}.
\left(\frac{\frac{81}{289}}{\frac{81}{16}\times \frac{2}{5}}\right)^{-1}
Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.
\left(\frac{\frac{81}{289}}{\frac{81}{40}}\right)^{-1}
Multiply \frac{81}{16} and \frac{2}{5} to get \frac{81}{40}.
\left(\frac{81}{289}\times \frac{40}{81}\right)^{-1}
Divide \frac{81}{289} by \frac{81}{40} by multiplying \frac{81}{289} by the reciprocal of \frac{81}{40}.
\left(\frac{40}{289}\right)^{-1}
Multiply \frac{81}{289} and \frac{40}{81} to get \frac{40}{289}.
\frac{289}{40}
Calculate \frac{40}{289} to the power of -1 and get \frac{289}{40}.
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