A) a^5 a^8, б) a^8: a^5 B) (а^5)^8 г)(а^3)^2*а^15/а^17

Let's simplify each of the expressions step by step.

a) \( a^5 \cdot a^8 \)

When multiplying expressions with the same base, you add the exponents: \[ a^5 \cdot a^8 = a^{5 + 8} = a^{13} \]

б) \( \frac{a^8}{a^5} \)

When dividing expressions with the same base, you subtract the exponents: \[ \frac{a^8}{a^5} = a^{8 - 5} = a^{3} \]

B) \( (a^5)^8 \)

When raising a power to another power, you multiply the exponents: \[ (a^5)^8 = a^{5 \cdot 8} = a^{40} \]

г) \( \frac{(a^3)^2 \cdot a^{15}}{a^{17}} \)

First, simplify \( (a^3)^2 \): \[ (a^3)^2 = a^{3 \cdot 2} = a^{6} \]

Now substitute this result back into the expression: \[ \frac{a^{6} \cdot a^{15}}{a^{17}} \]

Next, simplify the numerator: \[ a^{6} \cdot a^{15} = a^{6 + 15} = a^{21} \]

Now you have: \[ \frac{a^{21}}{a^{17}} = a^{21 - 17} = a^{4} \]

Final results:

• a) \( a^{13} \)
• б) \( a^{3} \)
• B) \( a^{40} \)
• г) \( a^{4} \)