If `x^(4)=16`, what is `|x|`?

Answer

To solve the equation \( x^4 = 16 \) and find \( |x| \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ x^4 = 16 \]

### Step 2: Express 16 as a power of 2
We can express 16 as a power of 2:
\[ 16 = 2^4 \]
So, we can rewrite the equation as:
\[ x^4 = 2^4 \]

### Step 3: Take the fourth root of both sides
To solve for \( x \), we take the fourth root of both sides:
\[ x = \sqrt[4]{2^4} \]
This simplifies to:
\[ x = 2 \quad \text{or} \quad x = -2 \]
(since taking the fourth root gives both positive and negative solutions).

### Step 4: Calculate the absolute value
Now, we need to find \( |x| \):
\[ |x| = |2| = 2 \quad \text{or} \quad |x| = |-2| = 2 \]

### Final Answer
Thus, the value of \( |x| \) is:
\[ |x| = 2 \]

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