Answer:
D choice
Step-by-step explanation:
From:
[tex] \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{9}{6} \cdot \frac{ {a}^{4} }{ {a}^{7} }}[/tex]
9/6 can be simplified as 3/2.
[tex] \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot \frac{ {a}^{4} }{ {a}^{7} }}[/tex]
Law of Exponent
[tex] \displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }[/tex]
Therefore:
[tex] \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot {a}^{4 - 7} } \\ \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot {a}^{ - 3} } \\ [/tex]
Law of Exponent II
[tex] \displaystyle \large{ {a}^{ - n} = \frac{1}{ {a}^{n} } }[/tex]
Therefore:
[tex] \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot \frac{1}{ {a}^{3} }}[/tex]
Now, multiply.
[tex] \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2 {a}^{3} } }[/tex]
