Question

Evaluate:

`[216^(2/3) + 64^(1/3) * 49^(1/2)]^((-1)/3)`

Answer 1

Let’s evaluate:

`[216^(2/3) + 64^(1/3) * 49^(1/2)]^(-1/3)`

Step 1: Simplify each term

`216^(2/3) = (root(3)(216))^2 = 6^2 = 36`

`64^(1/3) = root(3)(64) = 4`

`49^(1/2) = sqrt(49) = 7`

Now multiply:

`4 * 7 = 28`

Step 2: Add inside the brackets

36 + 28 = 64

Step 3: Apply the outer exponent

`64^(-1/3) = 1/root(3)(64) = 1/4`