Question

`root(4)(16^-2)` = ______.

Options

• 4

• `1/4`

• – 4

• 2

Answer 1

`root(4)(16^-2) = underlinebb(1/4)`.

Explanation:

We are given the expression:

`root(4)(16^-2)`

Let’s break it down step by step:

Step 1: Express 16 as a power of 2

16 = 2⁴

So, we can rewrite 16^–2 as:

16^–2 = (2⁴)^–2 = 2^–8

Step 2: Take the fourth root of 2^–8

The fourth root of 2^–8 is:

`root(4)(2^-8) = 2^(-8//4) = 2^-2`

Step 3: Simplify

`2^-2 = 1/2^2 = 1/4`

Thus, the value of the expression is `1/4`.