F.3 數學 (指數) 急~

1. (a^2)^3 (a^2)
= a^(2*3) * a^2
= a^6 * a^2
= a^(6+2)
= a^8
2. (2b^2)^3 (4b^3)^2
= (2^3)b^6 * (4^2)b^6
= 8b^6 * 16b^6
= 128b^12
3. (x/y^2)^4 (y/x)^3
= (x^4)/(y^8) * (y^3)/x^3
= x / y^5
4. (3a^4．2a^2)^3 / a^3
= (6a^6)^3 / a^3
= 216a^18 / a^3
= 216a^15

5. (ab^2 c^3)^4 / abc
= (a^4)(b^8)(c^12) / abc
= a^3 b^7 c^11

6. (2ab)(ab)^2(bc)^2 / a^2 b^2 c^2
= 2(a^3)(b^3) (bc)^2 / a^2 b^2 c^2
= 2(a^3)(b^5)(c^2) / ( a^2 b^2 c^2)
= 2ab^3
7.
= 2^(3n+1) / 8^n
= 2(2^3n) / 8^n
= 2(8^n) / 8^n
= 2
8. 3^(n+1)．3^(n+2) / 3^(2n+1)
= 3(3^n) * (3^2)(3^n) / [3 (3^2n) ]
= 27 (3^n)^2 / [3 (3^n)^2]
= 27/3
= 9