\#6 i Evaluate the expression \( \frac{3^{4}}{3^{5}} \) \( \square \)

To simplify the expression \( \frac{3^{4}}{3^{5}} \), we can use the laws of exponents. When you divide two powers with the same base, you subtract the exponents: \[ \frac{3^{4}}{3^{5}} = 3^{4-5} = 3^{-1} \] Now, \( 3^{-1} \) is equal to \( \frac{1}{3} \). Thus, the final answer is \( \frac{1}{3} \). To further understand how exponents work, think of \( 3^{-1} \) as the inverse of \( 3^1 \). In practical terms, this reflects the concept of division and can be applied in various scenarios, such as in calculating probabilities or simplifying fractions in everyday math.