Question

complete the table with equivalent expressions. try another. rewrite \\(\frac{1}{10^{10}}\\), or \\(\frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10}\\), using a single power of 10.

single power of 10	expanded	fraction
\\(10\square\\)	\\(\frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10} \cdot \frac{1}{10}\\)	\\(\frac{1}{10^{10}}\\)

Explanation:

Step1: Recall negative exponent rule

The rule is \( \frac{1}{a^n} = a^{-n} \), where \( a
eq 0 \) and \( n \) is a positive integer.

Step2: Apply the rule to \( \frac{1}{10^{10}} \)

Here, \( a = 10 \) and \( n = 10 \). Using the rule \( \frac{1}{10^{10}} = 10^{-10} \).

Answer:

\( 10^{-10} \) (so the box should be filled with \(-10\))