Question

c. \\(\frac{9^{14}}{9^7}\\)\
2 a certain type of bacteria reproduces so that after x hours there are \\(15^x\\) cells. what single power represents the size relationship between the cell population after 24 hours and the cell population after 8 hours? show your work.

Explanation:

Step1: Find population at 24 and 8 hours

Population at \( x = 24 \) hours: \( 15^{24} \)
Population at \( x = 8 \) hours: \( 15^{8} \)

Step2: Find the ratio (relationship)

To find the relationship, divide the population at 24 hours by the population at 8 hours:
\( \frac{15^{24}}{15^{8}} \)
Using the exponent rule \( \frac{a^m}{a^n}=a^{m - n} \), where \( a = 15 \), \( m = 24 \), \( n = 8 \)
\( 15^{24-8}=15^{16} \)

Answer:

\( 15^{16} \)