Question

what is $10^2$ divided by $10^5$? $10^{-3}$ or $\frac{1}{10^3}$ $10^{-10}$ $10^3$ rewatch

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base, we use the rule \( \frac{a^m}{a^n} = a^{m - n} \). Here, \( a = 10 \), \( m = 2 \), and \( n = 5 \).
\( \frac{10^2}{10^5} = 10^{2 - 5} \)

Step2: Calculate the exponent

Simplify the exponent: \( 2 - 5 = -3 \), so \( 10^{2 - 5} = 10^{-3} \). We also know that \( a^{-n} = \frac{1}{a^n} \), so \( 10^{-3} = \frac{1}{10^3} \).

Answer:

\( 10^{-3} \) or \( \frac{1}{10^3} \) (the first option)