Question

`[27^(1//3) + 8^(1//3)]^-3` = ______.

Options

• 125

• `1/125`

• 35

• `1/35`

Answer 1

`[27^(1//3) + 8^(1//3)]^-3 = underlinebb(1/125)`.

Explanation:

The expression provided is `(27^(1//3) + 8^(1//3))^-3`

Let’s break it down:

1. Cube roots:

• `27^(1//3) = 3` ...(Since 27 = 3³)
• `8^(1//3) = 2`  ...(Since 8 = 2³)

So, the expression becomes (3 + 2)^–3

2. Simplify:

• 3 + 2 = 5

Thus, we have 5^–3

3. Final calculation:

• `5^-3 = 1/5^3 = 1/125`