Find the value of each of the following: i) 16^1/4 ii) 625^3/4

To find the values of the given expressions, we can break them down step by step.

i) 16^1/4

Here, we want to find the fourth root of 16. The number 16 can be expressed as 2⁴ (since 2 x 2 x 2 x 2 = 16). When we take the fourth root, we essentially want to find a number that, when raised to the power of 4, equals 16. This number is 2, since 2⁴ = 16.

Thus, 16^1/4 = 2.

ii) 625^3/4

To find this value, we can first find the fourth root of 625 and then cube that result. The number 625 can be expressed as 25², and 25 can be further expressed as 5². Therefore, 625 can also be represented as (5²)² = 5⁴. Taking the fourth root of 625 gives us 5 (because 5⁴ = 625).

Now we take this result (5) and raise it to the power of 3: 5³ = 125.

Therefore, 625^3/4 = 125.

In summary:

• 16^1/4 = 2
• 625^3/4 = 125