Question #e299b

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Answer 1 · 2017-08-10T07:39:55

#- frac(7)(5)#

Let #x = frac(5)(- 7)#

"Multiplicative inverse" is a term that has the same meaning as "reciprocal".

So we are being asked to find #x^(- 1) = frac(1)(x)#:

#Rightarrow x^(- 1) = frac(1)(x)#

#Rightarrow x^(- 1) = frac(1)(frac(5)(- 7))#

#Rightarrow x^(- 1) = 1 cdot frac(- 7)(5)#

#therefore x^(- 1) = - frac(7)(5)#

Therefore, the multiplicative inverse of #frac(5)(- 7)# is #- frac(7)(5)#.