Question

which expression is equivalent to \\(\frac{10^{-9}}{10^{3}}\\)?\
\\(10^{-3}\\) \\(10^{-12}\\)\
\\(10^{-6}\\) \\(\frac{1}{10^{-3}}\\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we subtract the exponents: $\frac{a^m}{a^n} = a^{m - n}$. Here, the base is 10, $m = -9$, and $n = 3$.

Step2: Apply the rule

Calculate $-9 - 3 = -12$. So $\frac{10^{-9}}{10^{3}} = 10^{-12}$.

Answer:

$10^{-12}$ (corresponding to the option with $10^{-12}$)