By what number should `3^(-3)` be multiplied to obtain 4?

Answer

To solve the problem of finding the number by which \(3^{-3}\) should be multiplied to obtain 4, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equation**:
We need to find a number \(x\) such that:
\[ 3^{-3} \times x = 4 \]

2. **Rewrite the Negative Exponent**:
Recall that a negative exponent means the reciprocal. Therefore:
\[ 3^{-3} = \frac{1}{3^3} \]
So we can rewrite the equation as:
\[ \frac{1}{3^3} \times x = 4 \]

3. **Calculate \(3^3\)**:
Now, calculate \(3^3\):
\[ 3^3 = 3 \times 3 \times 3 = 27 \]
Substitute this back into the equation:
\[ \frac{1}{27} \times x = 4 \]

4. **Isolate \(x\)**:
To isolate \(x\), multiply both sides of the equation by 27:
\[ x = 4 \times 27 \]

5. **Calculate \(4 \times 27\)**:
Now, calculate \(4 \times 27\):
\[ 4 \times 27 = 108 \]

6. **Final Answer**:
Therefore, the number by which \(3^{-3}\) should be multiplied to obtain 4 is:
\[ x = 108 \]

### Summary:
To obtain 4 by multiplying \(3^{-3}\), we need to multiply it by 108.

---