F3 maths::指數定律::(10點)

1. (2d^3e^2)^4
= 2^4 d^12 e^8
= 16 d^12 e^8

2.(-2x^3y^2z)^2
= 4 x^6 y^4 z^2

3.(-x/3y)^3
= -x^3/ 9y^3

4.(2m/n^4p)^4
= 16m^4 / n^16 p^4

5.[(-c^2)^3]^4
= (-c^2)^12
= c^24

6. [-(p^3)^2/q^4]
= -p^6/q^4

7. a^2 ×(a^3)^4 ×-a^3
= a^2 x a^12 x -a^3
= -a^(2+12+3)
= -a^17

8. (b^5)^3 ÷(b^2)^2 ÷(b^3)^2
= b^(15-4-6)
= b^5

9. (ab)^4 ×(a^2b^2)^3
= a^(4+ 2*3) b^(4+ 2*3)
= a^10 b^10

10. (-a^2b)^3 /(-ab)^2
= -a^6 b^3 / -a^2 b^2
= a^(6-2) b^(3-2)
= a^4 b

11. (x^2y)^2 ×(x/y^3)^3
= (x^4 y^2) X (x^3/y^9)
= x^(4+3) y(2-9)
= x^7/y^7

12. (a/b)^3 ×(b/a)^2
= (a^3/b^3) X (b^2/a^2)
= a^(3-2) b^(2-3)
= a/b

13. (m/-n^2)^2 ×(n/m^2)^3
= (m^2/n^4) X (n^3/m^6)
= m^(2-6) n^(3-4)
= 1/ m^4 n

14. (ab^3)^4 ×(-c)^13 /(-ac^6)^2
= a^4b^12 X -c^13/a^2c^12
= -a^(4-2) b^12 c^(13-12)
= -a^2 b^12 c

15.p^2q^3 ×(-pq^2r^3) ÷p^3q^4r
= -p^(2+1-3) q^(3+2-4) r^(3-1)
= -q r^2

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