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\sqrt[4]{25^{-2}}
Use the rules of exponents to simplify the expression.
25^{-2\times \frac{1}{4}}
To raise a power to another power, multiply the exponents.
25^{-\frac{1}{2}}
Multiply -2 times \frac{1}{4}.
\frac{1}{5}
Raise 25 to the power -\frac{1}{2}.