Answer
$\frac{15}{16}$
Work Step by Step
We are given the expression $1^{-3}-4^{-2}$
$1^{-3}-4^{-2}=\frac{1}{1^{3}}-\frac{1}{4^{2}}=1-\frac{1}{16}=\frac{16}{16}-\frac{1}{16}=\frac{15}{16}$
In general, $a^{-n}=\frac{1}{a^{n}}$ (where a is a nonzero real number and n is a positive integer).