For each of these statement, indicate whether the statement is TRUE or FALSE
If `x^4 = 16`, then `x = 2`

Answer

To determine whether the statement "If \( x^4 = 16 \), then \( x = 2 \)" is true or false, we can follow these steps:

### Step 1: Analyze the equation
We start with the equation given in the statement:
\[ x^4 = 16 \]

### Step 2: Solve for \( x \)
To solve for \( x \), we can take the fourth root of both sides of the equation:
\[ x = \sqrt[4]{16} \]

### Step 3: Calculate the fourth root
We know that:
\[ 16 = 2^4 \]
Thus, taking the fourth root gives us:
\[ x = \sqrt[4]{2^4} = 2 \]

### Step 4: Consider negative roots
However, since we are dealing with an even power (4), we must also consider negative values. The fourth root can also be negative:
\[ x = -\sqrt[4]{16} = -2 \]

### Conclusion
From the calculations, we find that:
\[ x = 2 \quad \text{or} \quad x = -2 \]
Therefore, the statement "If \( x^4 = 16 \), then \( x = 2 \)" is **FALSE** because \( x \) can also be \( -2 \).

### Summary of the solution:
- The statement is FALSE because \( x \) can be \( 2 \) or \( -2 \).