1. The problem is to rewrite the expression $\left(\frac{7}{5}\right)^{-1}$ without an exponent. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$. 3. Applying this rule, we get: $$\left(\frac{7}{5}\right)^{-1} = \frac{1}{\left(\frac{7}{5}\right)^1} = \frac{1}{\frac{7}{5}}$$ 4. Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{1}{\frac{7}{5}} = 1 \times \frac{5}{7} = \frac{5}{7}$$ 5. Therefore, the expression without an exponent is $\frac{5}{7}$.