Express each of the following rational number in exponential form
` ( -1)/(512)`

Answer

To express the rational number \(-\frac{1}{512}\) in exponential form, we can follow these steps:

### Step 1: Factor 512
First, we need to express 512 as a power of 2. We can do this by continuously dividing 512 by 2 until we reach 1.

- \(512 \div 2 = 256\)
- \(256 \div 2 = 128\)
- \(128 \div 2 = 64\)
- \(64 \div 2 = 32\)
- \(32 \div 2 = 16\)
- \(16 \div 2 = 8\)
- \(8 \div 2 = 4\)
- \(4 \div 2 = 2\)
- \(2 \div 2 = 1\)

Counting the divisions, we see that \(512 = 2^9\).

### Step 2: Rewrite the Rational Number
Now that we know \(512 = 2^9\), we can rewrite the rational number \(-\frac{1}{512}\) as:
\[ -\frac{1}{512} = -\frac{1}{2^9} \]

### Step 3: Express in Exponential Form
The expression \(-\frac{1}{2^9}\) can be rewritten using negative exponents:
\[ -\frac{1}{2^9} = -1 \cdot 2^{-9} \]

Thus, the exponential form of \(-\frac{1}{512}\) is:
\[ -1 \cdot 2^{-9} \]

### Final Answer
So, the final answer is:
\[ -\frac{1}{512} = -1 \cdot 2^{-9} \]

---