Final answer:
The simplified form of the fraction is k⁶ / 8.
Step-by-step explanation:
To simplify the fraction k⁹ / 8k³, we can divide both the numerator and denominator by the highest power of the variable k that appears in both terms.
In this case, the highest power of k is k³.
Dividing both terms by k³, we get:
k⁹ / 8k³ = (k⁹ / k³) / (8 / 1) = k⁶ / 8
The fraction k⁹ / 8k³, when simplified, is k⁶ / 8.