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4^{\frac{5}{8\times 100}}
Express \frac{\frac{5}{8}}{100} as a single fraction.
4^{\frac{5}{800}}
Multiply 8 and 100 to get 800.
4^{\frac{1}{160}}
Reduce the fraction \frac{5}{800} to lowest terms by extracting and canceling out 5.