To represent the given expression as a power of the number \(a\), first simplify the expression inside the parentheses and then apply the negative exponent.
Inside the parentheses, simplify:
\[
a^5 \times \frac{a}{a^{-3}}
\]
To divide with the same base (in this case, \(a\)), subtract the exponents:
\[
a^{5-(-3)} = a^8
\]
Now, the expression inside the parentheses simplifies to \(a^8\).
The given expression is now \((a^8)^{-1}\). When you raise a power to a negative exponent, you invert the base and change the exponent sign.
\[
(a^8)^{-1} = a^{-8}
\]
Therefore, the given expression, \((a^5 \times \frac{a}{a^{-3}})^{-1}\), can be represented as \(a^{-8}\).