$$ \begin{aligned} 7x+\frac{1}{5^0} &= 0&& \text{multiply ALL terms by } \color{blue}{ 1 }. \\[1 em]1\cdot7x+1\cdot\frac{1}{5^0} &= 1\cdot0&& \text{cancel out the denominators} \\[1 em]7x+1 &= 0&& \text{ move the constants to the right } \\[1 em]7x &= -1&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= -\frac{1}{7}&& \\[1 em] \end{aligned} $$

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