Answer
The answer is $a^{-4}$
Work Step by Step
To solve this
$a^{0}$=1 as any number with exponent 0 becomes 1
$a^{x}$ $\times$ $a^{4}$ = 1
$a^{x}$ $\times$ $a^{4}$ = $a^{0}$
$a^{x}$ = $\frac{a^{0}}{a^{4}}$
$a^{x}$ = $a^{0-4}$
$a^{x}$ = $a^{-4}$ --> same base, bring the exponents down
x= -4
Therefore the missing part is $a^{-4}$.