What is $\left(\frac{7}{8}\right)^3 \cdot \left(\frac{7}{8}\right)^{-3}$?
To solve this problem, I need to apply the rules of exponents for multiplying powers with the same base. I can rewrite the expression as $\left(\frac{7}{8}\right)^{3 + (-3)}$. Adding the exponents, I get $\left(\frac{7}{8}\right)^0$. Any nonzero number raised to the zero power is equal to one. Therefore, the answer is 1. 