01 $a^3 \times a^5 = a^{3+5} = a^8$

02 $(a^2)^5 = a^{2 \times 5} = a^{10}$

03 $(ab)^4 = a^4 b^4$

04 $a^9 \div a^4 = a^{9-4} = a^5$

05 $a^5 \div a^5 = a^{5-5} = a^0 = 1$

06 $a^3 \div a^7 = a^{3-7} = a^{-4} = \dfrac{1}{a^4}$

07 $a^2 b^3 \times a^5 b^2 = a^{2+5} b^{3+2} = a^7 b^5$

08 $x^3 \times x^2 y \times y^4 = x^{3+2} y^{1+4} = x^5 y^5$

09 $(a^2 b)^3 \times (ab^3)^2 = a^6 b^3 \times a^2 b^6 = a^{6+2} b^{3+6} = a^8 b^9$

10 $\left(\dfrac{a^2}{b}\right)^3 \times \left(\dfrac{b}{a}\right)^4 = \dfrac{a^6}{b^3} \times \dfrac{b^4}{a^4} = \dfrac{a^{6-4} \cdot b^{4-3}}{1} = a^2 b$

11 $(-3a^2 b^3)^3 \div (3ab)^2 = (-27a^6 b^9) \div (9a^2 b^2)$
  $= \dfrac{-27}{9} \cdot a^{6-2} \cdot b^{9-2} = -3a^4 b^7$

12 $4a^5 b^3 \times 2a^2 b \div \left(\dfrac{a^3}{b}\right)^2 = 8a^7 b^4 \div \dfrac{a^6}{b^2}$
  $= 8a^7 b^4 \times \dfrac{b^2}{a^6} = 8a^{7-6} b^{4+2} = 8ab^6$