Final answer:
The value of 16³/4 is found by first cubing 16 to get 4096, and then taking the fourth root of 4096 which is 4.
Step-by-step explanation:
To find the value of 16³/4, we need to understand that it asks for the fourth root of 16 cubed. According to the laws of exponents, a fractional exponent like 3/4 means that we first raise the number to the numerator's power and then take the denominator's root of the result (or vice versa, as it yields the same answer).
Let's break down the solution:
- Raise 16 to the third power: 16³ = 16 × 16 × 16 = 4096.
- Take the fourth root of 4096, which means finding a number that when raised to the fourth power gives 4096. The fourth root of 4096 is 4 because 4 × 4 × 4 × 4 = 4096.
Therefore, the value of 16³/4 is 4.