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\sqrt[40]{10^{2}}
Rewrite 100 as 10^{2}.
\left(10^{2}\right)^{\frac{1}{40}}
Convert from radical to exponential form.
10^{\frac{2}{40}}
To raise a power to another power, multiply the exponents.
10^{\frac{1}{20}}
Reduce the fraction \frac{2}{40} to lowest terms by extracting and canceling out 2.
\sqrt[20]{10}
Convert from exponential to radical form.