Question

Help me with this question

Answer 1

Answer:

D choice

Step-by-step explanation:

From:

$\displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{9}{6} \cdot \frac{ {a}^{4} }{ {a}^{7} }}$

9/6 can be simplified as 3/2.

$\displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot \frac{ {a}^{4} }{ {a}^{7} }}$

Law of Exponent

$\displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

Therefore:

$\displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot {a}^{4 - 7} } \\ \displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot {a}^{ - 3} }$

Law of Exponent II

$\displaystyle \large{ {a}^{ - n} = \frac{1}{ {a}^{n} } }$

Therefore:

$\displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2} \cdot \frac{1}{ {a}^{3} }}$

Now, multiply.

$\displaystyle \large{ \frac{ {9a}^{4} }{ {6a}^{7} } = \frac{3}{2 {a}^{3} } }$