To what power (-2) should be raised to get 16?

Answer

To solve the question "To what power should (-2) be raised to get 16?", we can follow these steps:

### Step 1: Understand the Problem
We need to find the exponent \( n \) such that:
\[ (-2)^n = 16 \]

### Step 2: Express 16 as a Power of 2
First, we can express 16 as a power of 2. We know:
\[ 16 = 2^4 \]

### Step 3: Relate \( (-2)^n \) to \( 2^4 \)
Since \( (-2)^n \) can be expressed in terms of \( 2^n \), we can rewrite the equation:
\[ (-2)^n = 2^4 \]
We know that if \( n \) is even, \( (-2)^n \) will equal \( 2^n \). Therefore, we can set:
\[ 2^n = 2^4 \]

### Step 4: Equate the Exponents
Since the bases are the same, we can equate the exponents:
\[ n = 4 \]

### Step 5: Conclusion
Thus, the power to which \(-2\) must be raised to get \(16\) is:
\[ \boxed{4} \]