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To convert this logarithmic equation to exponential form, let’s examine the equation:

\[
\log \left(\frac{1}{100,000,000}\right) = -8
\]

### Step 1: Recall the definition of a logarithm
The equation \(\log(a) = b\) can be rewritten in exponential form as:
\[
10^b = a
\]

### Step 2: Apply this definition
In this case:
\[
b = -8 \quad \text{and} \quad a = \frac{1}{100,000,000}
\]

So, we rewrite it as:
\[
10^{-8} = \frac{1}{100,000,000}
\]

### Final Answer
The exponential form of the equation is:
\[
10^{-8} = \frac{1}{100,000,000}
\]

Would you like further details or have any questions?

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### Related Questions
1. How do you convert other logarithmic forms to exponential forms?
2. What is the process of simplifying negative exponents?
3. How does changing the base of the logarithm affect the exponential form?
4. What is the relationship between logarithmic and exponential functions?
5. How would this equation change if it were a natural logarithm (\(\ln\)) instead?

### Tip
Remember that logarithmic functions and exponential functions are inverses, so converting between them simply involves “undoing” the logarithmic operation.

Write the equation in exponential form.
\[ \log \left(\frac{1}{100,000,000}\right) = -8 \]

Learn how to convert the logarithmic equation \( \log \left(\frac{1}{100,000,000}\right) = -8 \) to exponential form. This solution provides a step-by-step explanation of logarithmic and exponential conversions, suitable for high school students in grades 9-12.

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