Aus Online Mathematik Brückenkurs 1

When a power expression has a negative exponent, the expression's value decreases when the base increases. Thus

\displaystyle 0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}.

Another way to see this is to rewrite the two powers as

\displaystyle 0\textrm{.}5^{-3}=\frac{1}{0\textrm{.}5^{3}}\quad and \displaystyle \quad 0\textrm{.}4^{-3}=\frac{1}{0\textrm{.}4^3}

and because \displaystyle 0\textrm{.}5^{3} > 0\textrm{.}4^{3} (see exercise a), it follows that

\displaystyle \frac{1}{0\textrm{.}4^{3}} > \frac{1}{0\textrm{.}5^{3}}\,,

i.e. \displaystyle 0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}\,.