To determine which of the given fractions correctly simplifies [tex]\(10^{-8}\)[/tex], let's analyze each of them step by step:
The given exponent form is [tex]\(10^{-8}\)[/tex]. We want to express this in fraction form.
1. Understanding [tex]\(10^{-8}\)[/tex]:
- By definition, [tex]\(10^{-8}\)[/tex] is equivalent to [tex]\(\frac{1}{10^8}\)[/tex].
2. Express each choice to check if it matches [tex]\(10^{-8}\)[/tex]:
- Choice 1: [tex]\(\frac{1}{-100,000,000}\)[/tex]
- This simplifies to [tex]\(-1 \times 10^{-8}\)[/tex] or [tex]\(-1e-08\)[/tex].
- Choice 2: [tex]\(\frac{1}{100,000,000}\)[/tex]
- This simplifies to [tex]\(1 \times 10^{-8}\)[/tex] or [tex]\(1e-08\)[/tex].
- Choice 3: [tex]\(\frac{1}{-80}\)[/tex]
- This does not simplify to any power of 10. Specifically, it gives a value of [tex]\(-0.0125\)[/tex].
- Choice 4: [tex]\(\frac{1}{80}\)[/tex]
- Similarly, this does not simplify to any power of 10. Specifically, it gives a value of [tex]\(0.0125\)[/tex].
3. Comparing each choice with [tex]\(10^{-8}\)[/tex]:
- [tex]\(10^{-8}\)[/tex] is [tex]\(1e-08\)[/tex].
- Among the choices, only [tex]\(\frac{1}{100,000,000}\)[/tex] matches [tex]\(1e-08\)[/tex].
Thus, the simplified form of [tex]\(10^{-8}\)[/tex] is [tex]\(\frac{1}{100,000,000}\)[/tex].
