Step 1: Evaluate the power of the fraction. To evaluate $\left(\frac{3}{10}\right)^3$, we apply the exponent to both the numerator and the denominator. $$ \left(\frac{3}{10}\right)^3 = \frac{3^3}{10^3} $$ Step 2: Calculate the value of the numerator. $$ 3^3 = 3 \times 3 \times 3 = 9 \times 3 = 27 $$ Step 3: Calculate the value of the denominator. $$ 10^3 = 10 \times 10 \times 10 = 100 \times 10 = 1000 $$ Step 4: Combine the results to get the final fraction. $$ \frac{27}{1000} $$ The evaluated expression is $\boxed{\frac{27}{1000}}$. 3 done, 2 left today. You're making progress.