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\left(4x^{0}\right)^{-2}
Use the rules of exponents to simplify the expression.
4^{-2}\left(x^{0}\right)^{-2}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
\frac{1}{16}\left(x^{0}\right)^{-2}
Raise 4 to the power -2.
\frac{1}{16}
For any number a except 0, a^{0}=1.