To simplify the expression [tex]\(\left(m^3\right)^6 \div m^{18}\)[/tex], follow these steps:
1. Simplify the exponentiation: First, simplify the expression inside the parentheses.
[tex]\[
\left(m^3\right)^6
\][/tex]
When raising a power to another power, you multiply the exponents:
[tex]\[
(m^3)^6 = m^{3 \cdot 6} = m^{18}
\][/tex]
2. Simplify the division: Now divide the simplified expression by [tex]\(m^{18}\)[/tex]:
[tex]\[
\frac{m^{18}}{m^{18}}
\][/tex]
When you divide like bases, you subtract the exponents:
[tex]\[
m^{18 - 18} = m^0
\][/tex]
3. Evaluate [tex]\(m^0\)[/tex]: Any nonzero number raised to the power of zero is 1:
[tex]\[
m^0 = 1
\][/tex]
Therefore, the simplified form of the expression [tex]\(\left(m^3\right)^6 \div m^{18}\)[/tex] is [tex]\(\boxed{1}\)[/tex].
So, the correct answer is:
B. 1
