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(iii) [tex]\((321 \times 567)^{-1} = (321)^{-1} \times (567)^{-1}\)[/tex]

Sagot :

GinnyAnswer
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]
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