Let's solve the given mathematical expression step-by-step:
We start with the expression:
[tex]\[
(321 \times 567)^{-1} = (321)^{-1} \times (?)
\][/tex]
To simplify this, we use the property of reciprocals for products. The property states:
[tex]\[
(a \times b)^{-1} = a^{-1} \times b^{-1}
\][/tex]
Applying this property to our given expression:
[tex]\[
(321 \times 567)^{-1} = (321)^{-1} \times (567)^{-1}
\][/tex]
Therefore, the expression [tex]\( (321 \times 567)^{-1} \)[/tex] can be broken down into:
[tex]\[
(321)^{-1} \times (567)^{-1}
\][/tex]
This shows us the missing part of the expression. Consequently, the complete simplified expression is:
[tex]\[
(321 \times 567)^{-1} = (321)^{-1} \times (567)^{-1}
\][/tex]
Therefore, the missing part is [tex]\( (567)^{-1} \)[/tex].
So, the final answer is:
[tex]\[
(321 \times 567)^{-1} = (321)^{-1} \times (567)^{-1}
\][/tex]
