F.3 maths(指數)

1.
(-5)^3 / 25^2
= -5^3 / (5^2)^2
= -5^3 / 5^4
= -5^(3-4)
= -5^-1
= -1 / 5


2.
(-6)^-2/3^-3
= [(-6)^2]^-1 / 3^-3
= 2^-2 * 3^-2 / 3^-3
= 2^-2 * 3^(-2+3)
= (1/4) * 3
= 3 / 4


3.
[(-2^3)^-1 * 4^3]^2
= [-2^-3 * (2^2)^3]^2
= (-2^-3 * 2^6)^2
= [-2^(-3+6)]^2
= (-2^3)^2
= 2^6
= 64


4.
3^-4 * 9^-3 / 27^-5
= 3^-4 * (3^2)^-3 / (3^3)^-5
= 3^-4 * 3^-6 / 3^-15
= 3^(-4-6+15)
= 3^5
= 243


5.
(2^5)^-1 / (-1/4)^3 x (16^-1)^2
= 2^-5 / [-(2^2)^-1]^3 x [(2^4)^-1]^2
= 2^5 / (-2^-6) x 2^-8
= -2^5+6+8
= -2^9
= -512


6.
(4 / 3^2)^-2 (3^-2 / 2^-1 )^3 + 2(3^-1)
= (2^2 3^-2)^-2 (3^-2 * 2)^3 + (2 / 3)
= 2^-4 3^4 3^-6 2^3 + (2 / 3)
= 2^(-4+3) 3^(4-6) + (2 / 3)
= 2^-1 3^-2 + (2 / 3)
= (1 / 18) + (12 / 18)
= 13 / 18


7.
(m^0)^-2
= 1^-2
= 1


8.
(c^0)^0
= 1^0
= 1


9.
(-2a)^-2
= 1 / (-2a)^2
= 1 / 4a^2


10.
a^5 a^3 / b^-4
= a^(5+3) (b^-4)^-1
= a^8 b^4


11.
(a^-4)^2 /a^-5
= a^-8 / a^-5
= a^(-8+5)
= a^-3
= 1 / a^3


12.
(a^-4)^3 / a^-10 a^2
= a^-12 / a^-10 a^2
= a^(-12+10-2)
= a^-4
= 1/a^4


13.
(m n^-1)^3 / n^-2
= m^3 n^-3 / n^-2
= m^3 n^(-3+2)
= m^3 n^-1
= m^3 / n


14.
m^-4 / (m^-3 n^-1)^2
= m^-4 / m^-6 n^-2
= m^(-4+6) (n^-2)^-1
= m^2 n^2


15.
(m^-1 n^3)^2 / m^-1 n^2
= m^-2 n^6 / m^-1 n^2
= m^(-2+1) n^(6-2)
= m^-1 n^4
= n^4 /m


16.
y^3 (x^-2)^-5 / (x^2 y)^4
= y^3 x^10 / x^8 y^4
= x^(10-8) y^(3-4)
= x^2 y^-1
= x^2 / y


17.
(a^3 b^-2)^-1 / (a^-2 b^4)^2
= a^-3 b^2 / a^-4 b^8
= a^(-3+4) b^(2-8)
= a b^-6
= a / b^6


18.
(x^-3 y^2 / x^2)^-2 (x^-1 y)^3
= (x^6 y^-4 / x^-4) (x^-3 y^3)
= x^(6+4-3) y^(-4+3)
= x^7 y^-1
= x^7 / y


19.
(-1/5)^2009 * 5^2010
= (-5^-1)^2009 * 5^2010
= -5^-2009 * 5^2010
= -5^(-2009+2010)
= -5


20.
若n是一個正整數，則
2^7n / (3^n)^2
= 2^7n / 3^2n


21.
81^m
= (9^2)^m
= (9^m)^2
= b^2

2013-08-26 20:37:27 補充：
20.
若題目是 2^7n / (2n)^2，則 2^7n / (2^n)^2
= 2^7n / 2^2n
= 2^(7n-5n)
= 2^2n

若題目是 3^7n / (3n)^2，則 3^7n / (3^n)^2
= 3^7n / 3^2n
= 3^(7n-5n)
= 3^2n

1.
(-5)^3/25^2
=-1/5

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

3.
〔(-2^3)^-1x4^3〕^2
=64

4.
3^-4x9^-3 /27^-5
=243

5.
(2^5 )^-1 /(-1/4)^3x(16^-1)^2
=1/128

6.
(4/3^2 )^-2 (3^-2 /2^-1 )^3 +2(3^-1 )
=13/18

7.
(m^0)^-2
=1

8.
(c^0)^0
=1

9.
(-2a)^-2
=1/(4a^2)

10.
a^5a^3 /b^-4
=a^8 b^4

11.
(a^-4)^2 /a^-5
=1/(a^3)

12.
(a^-4)^3 /a^-10 a^2
=1/(a^4)

13.
(mn^-1)^3/n^-2
=(m^3)/n

14.
m^-4/(m^-3n^-1)^2
=m^2 n^2

15.
(m^-1n^3)^2/m^-1n^2
=n^4/m

16.
y^3(x^-2)^-5/(x^2y)^4
=x^2/y

17.
(a^3b^-2)^-1/(a^-2b^4)^2
=a/(b^6)

18.
(x^-3y^2/x^2)^-2 (x^-1y)^3
=(y^2/x^5)^2 (y^3 /x^3)
=y^7 / x^13

19.
(-1/5)^2009 (5)^2010
=-5

20.
2^7n/(3^n)^2
=128^n/9^n
=(128/9)^n

21.
81^m
=9^(2m)
=b^2