Final answer:
To simplify the expression (−7 6/7 )−1 7/9, convert the mixed numbers to improper fractions and then use the rule (a/b)^c = (a^c)/(b^c).
Step-by-step explanation:
In order to simplify the expression (−7 6/7 )−1 7/9, we need to first convert the mixed numbers into improper fractions.
(−7 6/7 ) can be written as (-49/7).
Now, we can use the rule that states (a/b)^c = (a^c)/(b^c) to simplify the expression.
So, (-49/7)^(-1 7/9) can be written as (7/(-49))^(-1 7/9).
Applying the rule, this becomes (7^(-1 7/9))/((-49)^(-1 7/9)).
To simplify it further, we need to take the reciprocal of both the numerator and denominator.
So, the final answer is (-1/7^(1 7/9))/(1/(-49)^(1 7/9)).