Question

evaluate.
$10^{-8}$

Explanation:

Step1: Recall negative exponent rule

The rule for negative exponents is \( a^{-n}=\frac{1}{a^{n}} \) where \( a
eq0 \) and \( n \) is a positive integer. For \( 10^{-8} \), we apply this rule.

Step2: Apply the rule

Using the rule \( a^{-n}=\frac{1}{a^{n}} \) with \( a = 10 \) and \( n=8 \), we get \( 10^{-8}=\frac{1}{10^{8}} \).

Step3: Calculate \( 10^{8} \)

\( 10^{8}=10\times10\times10\times10\times10\times10\times10\times10 = 100000000 \).

Step4: Write the final form

So \( \frac{1}{10^{8}}=\frac{1}{100000000}=0.00000001 \).

Answer:

\( 10^{-8}=0.00000001 \) (or \( \frac{1}{100000000} \))