Question

cphs : advanced algebra: concepts and connections - block (27.0831030)
negative exponents
raising a power to a power
simplify $10^{-8}$.
options: $\frac{1}{100,000,000}$, $-\frac{1}{100,000,000}$, $\frac{1}{80}$, $-\frac{1}{80}$

Explanation:

Step1: Recall negative exponent rule

The rule for negative exponents is \( a^{-n} = \frac{1}{a^{n}} \) (where \( a
eq 0 \) and \( n \) is a positive integer). For \( 10^{-8} \), we apply this rule: \( 10^{-8}=\frac{1}{10^{8}} \).

Step2: Calculate \( 10^{8} \)

\( 10^{8} = 10\times10\times10\times10\times10\times10\times10\times10 = 100000000 \) (100 million). So \( \frac{1}{10^{8}}=\frac{1}{100000000} \).

Answer:

\(\frac{1}{100000000}\) (the option with \(\frac{1}{100000000}\))