Answer:
The first choice, [tex]11^{15}[/tex].
Step-by-step explanation:
The numerator, [tex]11^{18}[/tex], is equivalent to eighteen "[tex]11[/tex]" multiplied together:
[tex]11^{18} = \underbrace{11 \times 11 \times 11 \times 11 \times \cdots \times 11 \times 11}_{\text{$18$ in total}}[/tex].
On the other hand, the denominator, [tex]11^{3}[/tex], is equivalent to three "[tex]11[/tex]" multiplied with one another:
[tex]11^{3} = 11 \times 11 \times 11[/tex].
Dividing [tex]11^{18}[/tex] by [tex]11^{3}[/tex] would eliminate three "[tex]11[/tex]" from the numerator:
[tex]\begin{aligned}& \frac{11^{18}}{11^{3}} \\ =\; & \frac{(11 \times 11 \times 11) \times \overbrace{11 \times \cdots \times 11}^{\text{$(18 - 3)$ in total}}}{(11 \times 11 \times 11)} \\ =\; & \overbrace{11 \times \cdots \times 11}^{\text{$15$ in total}} \\ =\; & 11^{15}\end{aligned}[/tex].
In general, dividing an expression by [tex]y^{b}[/tex] ([tex]y \ne 0[/tex]) is equivalent to multiplying that expression by [tex]y^{-b}[/tex].
For example, in this question, dividing [tex]11^{18}[/tex] by [tex]11^{3}[/tex] would be equivalent to multiplying [tex]11^{18}\![/tex] by [tex]11^{-3}[/tex]. In other words:
[tex]\begin{aligned}& \frac{11^{18}}{11^{3}} \\ =\; & 11^{18} \times 11^{-3} \\ =\; & 11^{18 - 3} \\ =\; & 11^{15}\end{aligned}[/tex].
