Question

evaluate. write your answer as a whole number or as a simplified fraction.
\\(\frac{10^{-1}}{10^{0}} = \frac{\square}{\square}\\)

Explanation:

Step1: Use exponent rule for division

When dividing exponents with the same base, we subtract the exponents: \( \frac{a^m}{a^n} = a^{m - n} \). Here, \( a = 10 \), \( m = -1 \), and \( n = 6 \). So we have \( 10^{-1 - 6} \).

Step2: Calculate the exponent

\( -1 - 6 = -7 \), so the expression becomes \( 10^{-7} \). By the definition of negative exponents, \( a^{-n} = \frac{1}{a^n} \), so \( 10^{-7} = \frac{1}{10^7} \). And \( 10^7 = 10000000 \), so \( \frac{1}{10^7} = \frac{1}{10000000} \).

Answer:

\(\frac{1}{10000000}\)