The quotient of the given division operation is -343. The correct option is the first option -343
Division operation
From the question, we are to determine the quotient of the given division operation
The given expression is
[tex]\frac{(-7)^{2} }{(-7)^{-1} }[/tex]
= [tex](-7)^{2}\div (-7)^{-1}[/tex]
= [tex]49\div \frac{1}{-7}[/tex]
= [tex]49\times -7[/tex]
= -343
Hence, the quotient of the given division operation is -343. The correct option is the first option -343
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