To determine the exponent [tex]\( n \)[/tex] in the expression [tex]\( 10^5 \div 10^2 = 10^n \)[/tex], we can use the rules of exponents for division. Specifically, for any base [tex]\( a \)[/tex] and exponents [tex]\( m \)[/tex] and [tex]\( n \)[/tex],
[tex]\[
\frac{a^m}{a^n} = a^{m-n}
\][/tex]
Given the base is 10 and the exponents are 5 and 2 respectively, according to the exponent rule,
[tex]\[
\frac{10^5}{10^2} = 10^{5-2}
\][/tex]
Calculate the exponent [tex]\( 5 - 2 \)[/tex]:
[tex]\[
5 - 2 = 3
\][/tex]
So,
[tex]\[
10^5 \div 10^2 = 10^3
\][/tex]
Thus, the exponent [tex]\( n \)[/tex] is [tex]\( 3 \)[/tex].
Hence, the corrected scientific notation for [tex]\( 10^5 \div 10^2 \)[/tex] is [tex]\( 10^3 \)[/tex], and the exponent is:
[tex]\[ \boxed{3} \][/tex]
