[tex]a)\ \ (a^3)^6:a^{10}=a^{18}:a^{10}=a^{18-10}=a^8\\\\\\b)\ \ \dfrac{(a^3)^2\cdot(a^2)^3}{a^6:a^4}=\dfrac{a^6\cdot a^6}{a^2}=\dfrac{a^{12}}{a^2}=a^{12-2}=a^{10}\\\\\\c)\ \ \dfrac{(a^5\cdot a^4)^2}{(a^3:a^2)^4}=\dfrac{(a^9)^2}{(a^1)^4}=\dfrac{a^1^8}{a^4}=a^{18-4}=a^{14}\\\\\\d)\ \ \dfrac{(a^9\cdot a^3:a^4)^3}{a\cdot(a^3)^5}=\dfrac{(a^1^2:a^4)^3}{a\cdot a^1^5}=\dfrac{(a^8)^3}{a^1\cdot a^1^5}=\dfrac{a^2^4}{a^1^6}=a^{24-16}=a^8[/tex]
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[tex]a)\ \ (a^3)^6:a^{10}=a^{18}:a^{10}=a^{18-10}=a^8\\\\\\b)\ \ \dfrac{(a^3)^2\cdot(a^2)^3}{a^6:a^4}=\dfrac{a^6\cdot a^6}{a^2}=\dfrac{a^{12}}{a^2}=a^{12-2}=a^{10}\\\\\\c)\ \ \dfrac{(a^5\cdot a^4)^2}{(a^3:a^2)^4}=\dfrac{(a^9)^2}{(a^1)^4}=\dfrac{a^1^8}{a^4}=a^{18-4}=a^{14}\\\\\\d)\ \ \dfrac{(a^9\cdot a^3:a^4)^3}{a\cdot(a^3)^5}=\dfrac{(a^1^2:a^4)^3}{a\cdot a^1^5}=\dfrac{(a^8)^3}{a^1\cdot a^1^5}=\dfrac{a^2^4}{a^1^6}=a^{24-16}=a^8[/tex]