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Step 1:I'll solve this problem following the specified LaTeX and formatting guidelines:
Step 2:: Understand the Problem
The problem asks us to simplify the expression $$10^{-8}$$.
This involves understanding negative exponents.
Step 3:: Recall the Rule for Negative Exponents
The rule for negative exponents states that $$a^{-n} = \frac{1}{a^{n}}
Step 4:: Apply the Negative Exponent Rule
10^{-8} = \frac{1}{10^{8}}
Step 5:: Calculate the Value
\frac{1}{10^{8}} = \frac{1}{100,000,000}
Final Answer
Key Insights: - A negative exponent means we take the reciprocal of the base raised to the positive exponent - This moves the decimal point to the left by the number of the exponent - 10^{- 8} represents a very small number (one ten-millionth)
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