1. The problem is to understand the meaning of multiplying by $\frac{1}{3}$ in an exponent or power context. 2. When you multiply an exponent by $\frac{1}{3}$, it means raising the base to the power of that fraction. 3. For example, if you have $a^m$ and you multiply the exponent $m$ by $\frac{1}{3}$, it becomes $a^{m \times \frac{1}{3}} = a^{\frac{m}{3}}$. 4. Raising a number to the power of $\frac{1}{3}$ means taking the cube root of that number. 5. So, $a^{\frac{1}{3}} = \sqrt[3]{a}$, which is the cube root of $a$. 6. This operation is useful in many algebraic and geometric problems involving roots and fractional exponents. Final answer: Multiplying the exponent by $\frac{1}{3}$ converts the exponent into a cube root operation \n Example: $8^{\frac{1}{3}} = \sqrt[3]{8} = 2$.