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\left(-\frac{7+1}{7}\right)^{2}z=-1
Multiply 1 and 7 to get 7.
\left(-\frac{8}{7}\right)^{2}z=-1
Add 7 and 1 to get 8.
\frac{64}{49}z=-1
Calculate -\frac{8}{7} to the power of 2 and get \frac{64}{49}.
z=-\frac{49}{64}
Multiply both sides by \frac{49}{64}, the reciprocal of \frac{64}{49}.