Answer
$\frac{1}{x^{36}}$
Work Step by Step
We are given the expression $(x^{4})^{-9}$.
To simplify, we can use the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers).
$(x^{4})^{-9}=x^{4\times-9}=x^{-36}$
To simplify this into a positive exponent, we know that $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer).
Therefore, $x^{-36}=\frac{1}{x^{36}}$
