Final answer:
To evaluate 16³/⁴, find the fourth root of 16 (which is 2) and then raise it to the third power to get 8. To evaluate 125²/³, find the cube root of 125 (which is 5) and then square it to get 25.
Step-by-step explanation:
The question involves evaluating expressions with fractional exponents, specifically 16³/⁴ and 125²/³ without using a calculator. This concept falls within the realm of exponents and roots, commonly covered in algebra.
To evaluate 16³/⁴, we can break this down into two steps: finding the fourth root of 16, and then raising it to the third power. The fourth root of 16 is 2, because 2⁴ = 16. Taking 2 to the third power (2³) gives us 8. Therefore, 16³/⁴ equals 8.
Similarly, to evaluate 125²/³, we first find the cube root of 125, which is 5 because 5³ = 125. Then, we raise 5 to the second power (5²) to get 25. Therefore, 125²/³ equals 25.