Answer:
Step-by-step explanation:
The question was copied incorrectly. You need to put parentheses around the denominator.
answer: b
Given expression is [tex]\frac{45m^{-6}p^{2}v^{12}}{15m^{-2}p^{8}v^{-4}}[/tex].
[tex]\frac{a^{m}}{a^{n}}&=a^{m-n}\\\frac{1}{a^{m}}&=a^{-m}[/tex]
use the properties and simplify the expression.
[tex]\frac{45{{m}^{-6}}{{p}^{2}}{{v}^{12}}}{15{{m}^{-2}}{{p}^{8}}{{v}^{-4}}}=\left( \frac{45}{15} \right)\left( \frac{{{m}^{-6}}}{{{m}^{-2}}} \right)\left( \frac{{{p}^{2}}}{{{p}^{8}}} \right)\left( \frac{{{v}^{12}}}{{{v}^{-4}}} \right) \\ \\=\left( \frac{15\cdot 3}{15} \right)\left( {{m}^{-6-\left( -2 \right)}} \right)\left( {{p}^{2-8}} \right)\left( {{v}^{12-\left( -4 \right)}} \right) \\ \\=3\left( {{m}^{-6+2}} \right)\left( {{p}^{-6}} \right)\left( {{v}^{12+4}} \right) \\[/tex]
[tex]=3\left( {{m}^{-4}} \right)\left( {{p}^{-6}} \right)\left( {{v}^{16}} \right) \\ =\frac{3{{v}^{16}}}{{{m}^{4}}{{p}^{6}}}[/tex]
So, the correct option is [tex](b)[/tex].
The remaining options does not match with the obtained result.
For more information:
https://brainly.com/question/10546051
[tex]\begin{align*}\frac{a^{m}}{a^{n}}&=a^{m-n}\\\frac{1}{a^{m}}&=a^{-m} \end{align*}[/tex]
