To what power (-3) should be raised to get -243?

Answer

To solve the question "To what power should (-3) be raised to get -243?", we will follow these steps:

### Step 1: Understand the problem
We need to find the power \( n \) such that:
\[ (-3)^n = -243 \]

### Step 2: Express -243 as a power of 3
First, we need to factor -243. Since we are looking for a power of -3, we will express 243 in terms of 3:
\[ 243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^5 \]
Thus, we can write:
\[ -243 = -1 \times 243 = -1 \times 3^5 \]

### Step 3: Relate -243 to (-3)
Now we can express -243 in terms of (-3):
\[ -243 = (-3)^5 \]
This is because:
\[ (-3)^5 = -3 \times -3 \times -3 \times -3 \times -3 \]
When multiplying an odd number of negative numbers, the result is negative.

### Step 4: Set the equation
Now we can set our equation:
\[ (-3)^n = (-3)^5 \]

### Step 5: Solve for n
Since the bases are the same, we can equate the exponents:
\[ n = 5 \]

### Final Answer
Thus, the power to which (-3) should be raised to get -243 is:
\[ \boxed{5} \]

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