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\frac{1}{1000^{0.4}}
Use the rules of exponents to simplify the expression.
1000^{0.4\left(-1\right)}
To raise a power to another power, multiply the exponents.
1000^{-0.4}
Multiply 0.4 times -1.
\frac{10^{0.8}}{100}
Raise 1000 to the power -0.4.