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Olá Anna,
![\left[\left(2^4\right)^x\right]^{x+1}=\frac{1}{2}\\\\\left ( 2^{4x} \right )^{x+1}=2^{-1}\\\\2^{4x^2+4x}=2^{-1}\\\\4x^2+4x=-1\\\\4x^2+4x+1=0\\\\(2x+1)^2=0\\\\\boxed{x=-\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cleft%282%5E4%5Cright%29%5Ex%5Cright%5D%5E%7Bx%2B1%7D%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5Cleft+%28+2%5E%7B4x%7D+%5Cright+%29%5E%7Bx%2B1%7D%3D2%5E%7B-1%7D%5C%5C%5C%5C2%5E%7B4x%5E2%2B4x%7D%3D2%5E%7B-1%7D%5C%5C%5C%5C4x%5E2%2B4x%3D-1%5C%5C%5C%5C4x%5E2%2B4x%2B1%3D0%5C%5C%5C%5C%282x%2B1%29%5E2%3D0%5C%5C%5C%5C%5Cboxed%7Bx%3D-%5Cfrac%7B1%7D%7B2%7D%7D "\left[\left(2^4\right)^x\right]^{x+1}=\frac{1}{2}\\\\\left ( 2^{4x} \right )^{x+1}=2^{-1}\\\\2^{4x^2+4x}=2^{-1}\\\\4x^2+4x=-1\\\\4x^2+4x+1=0\\\\(2x+1)^2=0\\\\\boxed{x=-\frac{1}{2}}")
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