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Sagot :

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]

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