Question

use the properties of exponents to simplify the expression:

\frac{(a^5)^3}{a^7}

a.) a^{22}
b.) a^1
c.) a^{15}
d.) a^8

Explanation:

Apply the power of a power rule

$$ (a^5)^3 = a^{5 \times 3} = a^{15} $$

Apply the quotient rule of exponents

$$ \frac{a^{15}}{a^7} = a^{15 - 7} = a^8 $$

Answer:

• a.) \(a^{22}\)
• b.) \(a^1\)
• c.) \(a^{15}\)
• d.) \(a^8\) (Correct answer)