Question

question 15 (mandatory) (1 point)
write $\frac{8^{17}\times8^{8}}{8^{5}}$ as a single power.

a) $8^{131}$
b) $8^{20}$
c) $64^{30}$
d) $1^{20}$

Explanation:

Step1: Use product - rule of exponents

When multiplying powers with the same base \(a^m\times a^n=a^{m + n}\). So, \(8^{17}\times8^{8}=8^{17 + 8}=8^{25}\).

Step2: Use quotient - rule of exponents

When dividing powers with the same base \(\frac{a^m}{a^n}=a^{m - n}\). So, \(\frac{8^{25}}{8^{5}}=8^{25-5}\).

Step3: Calculate the exponent

\(8^{25 - 5}=8^{20}\).

Answer:

B. \(8^{20}\)