Answer:
[tex]\frac{ {6}^ { - 7}}{ {6}^{5} } = \frac{1}{{6}^{ 12}} [/tex]
Step-by-step explanation:
We want to simplify:
[tex] \frac{ {6}^{ - 7} }{ {6}^{5} } [/tex]
Since the bases are the same, we use the quotient rule of indices:
[tex] \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} [/tex]
We apply this rule to obtain:
[tex] \frac{ {6}^ { - 7}}{ {6}^{5} } = {6}^{ - 7 - 5} [/tex]
We simplify in the exponents to get:
[tex]\frac{ {6}^ { - 7}}{ {6}^{5} } = {6}^{ - 12} [/tex]
We rewrite as a positive index to get:
[tex]\frac{ {6}^ { - 7}}{ {6}^{5} } = \frac{1}{{6}^{ 12}} [/tex]
