33. Solve the equation \( 0.3^{3}=n \)

To solve the equation \( 0.3^{3} = n \), we simply need to calculate \( 0.3 \) raised to the power of \( 3 \). Calculating, we find: \[ 0.3^{3} = 0.3 \times 0.3 \times 0.3 = 0.027 \] Thus, \( n = 0.027 \). In a real-world context, understanding exponentiation like this is super useful when dealing with percentages in finance, scientific calculations, or even when interpreting data trends. For instance, if you're calculating compound interest or growth rates, you'll frequently encounter exponential functions! When working with powers and exponents, a common mistake is to misinterpret the notation. Be careful not to confuse \( 0.3^3 \) with \( 3 \times 0.3 \), as they yield very different results (the former is much smaller!). Always double-check your calculations to avoid such pitfalls!