Question

请教几道七年级数学题！急急急急急急急急急急！！！！！！！！！！

一个正方形的体积为8*10^12立方毫米,则它的棱长为多少毫米？（填空题，直接答案就行了！）
计算:-(a^2*b)*(2ab)^3+10*a^5*b^4（要过程的！）
计算:(-2x^2)*(-y)+3xy*(1-1/3x)（要过程的！）
已知x=[(-1)^n-(-1)^n+1]/2,求x+2x^2+3x^3+……+99x^99+100x^100的值。（要过程！此题为分类思想，两种情况！）
计算:8^8*(-1/4)^12（要过程的！还要简便方法！）

Answer 1

第一题（8+12+10）*4=120

第二题-(a^2*b)*(2ab)^3+10*a^5*b^4
= -a^2 * b * 8 * a^3 * b^3 + 10 * a^5 * b^4
= -8 * a^5 * b^4 + 10 * a^5 * b^4
= 2 * a^5 * b^4

第三题(-2x^2)*(-y)+3xy*(1-1/3x)
= 2 * x^2 * y + 3xy - x^2 * y
= x^2 * y + 3xy

第四题当n为奇数时 x = [(-1) - (1)]/2 = -1
S = x+2x^2+3x^3+……+99x^99+100x^100
= -1 + 2 - 3 + ... - 99 + 100
= 1 + 1 + ... + 1 (50项)
= 50
当n为偶数时 x = [1 - (-1)]/2 = 1
S = x+2x^2+3x^3+……+99x^99+100x^100
= 1 + 2 + 3 + ... + 99 + 100
= 100 * (1 + 100) / 2
= 5050

第五题(2^3)^8 * 2^(-2)^12* (-1)^12
=2^(3*8)* 2^(-24)*1
=1

Answer 2

（8+12+10）*4=120

-(a^2*b)*(2ab)^3+10*a^5*b^4
= -a^2 * b * 8 * a^3 * b^3 + 10 * a^5 * b^4
= -8 * a^5 * b^4 + 10 * a^5 * b^4
= 2 * a^5 * b^4

(-2x^2)*(-y)+3xy*(1-1/3x)
= 2 * x^2 * y + 3xy - x^2 * y
= x^2 * y + 3xy

当n为奇数时 x = [(-1) - (1)]/2 = -1
S = x+2x^2+3x^3+……+99x^99+100x^100
= -1 + 2 - 3 + ... - 99 + 100
= 1 + 1 + ... + 1 (50项)
= 50
当n为偶数时 x = [1 - (-1)]/2 = 1
S = x+2x^2+3x^3+……+99x^99+100x^100
= 1 + 2 + 3 + ... + 99 + 100
= 100 * (1 + 100) / 2
= 5050

(2^3)^8 * 2^(-2)^12* (-1)^12
=2^(3*8)* 2^(-24)*1
=1

2L的第一道和最后一道有问题，其它的没仔细看，你自己检查下吧，应该是对的。
我个去，二楼坑爹啊，第三道最后的那个3xy怎么变成2xy了……还好我看了下……

Answer 3

a^3 = 8*10^12 a = 2 * 10^4

-(a^2*b)*(2ab)^3+10*a^5*b^4
= -a^2 * b * 8 * a^3 * b^3 + 10 * a^5 * b^4
= -8 * a^5 * b^4 + 10 * a^5 * b^4
= 2 * a^5 * b^4

(-2x^2)*(-y)+3xy*(1-1/3x)
= 2 * x^2 * y + 3xy - x^2 * y
= x^2 * y + 2xy

当n为奇数时 x = [(-1) - (1)]/2 = -1
S = x+2x^2+3x^3+……+99x^99+100x^100
= -1 + 2 - 3 + ... - 99 + 100
= 1 + 1 + ... + 1 (50项)
= 50
当n为偶数时 x = [1 - (-1)]/2 = 1
S = x+2x^2+3x^3+……+99x^99+100x^100
= 1 + 2 + 3 + ... + 99 + 100
= 100 * (1 + 100) / 2
= 5050

8^8*(-1/4)^12
= (2^3)^3 * (1/4)^12
= (2^3)^3 / 4^12
= (2^3)^3/ (2^2)^12
= 2^(3*3) / 2^(2*12)
= 2^9 / 2^24
= 2^(9 - 24)
= 2^(-15)
= 1/ 2^15

Answer 4

（8+12+10）*4=120

-(a^2*b)*(2ab)^3+10*a^5*b^4
= -a^2 * b * 8 * a^3 * b^3 + 10 * a^5 * b^4
= -8 * a^5 * b^4 + 10 * a^5 * b^4
= 2 * a^5 * b^4

(-2x^2)*(-y)+3xy*(1-1/3x)
= 2 * x^2 * y + 3xy - x^2 * y
= x^2 * y + 3xy

当n为奇数时 x = [(-1) - (1)]/2 = -1
S = x+2x^2+3x^3+……+99x^99+100x^100
= -1 + 2 - 3 + ... - 99 + 100
= 1 + 1 + ... + 1 (50项)
= 50
当n为偶数时 x = [1 - (-1)]/2 = 1
S = x+2x^2+3x^3+……+99x^99+100x^100
= 1 + 2 + 3 + ... + 99 + 100
= 100 * (1 + 100) / 2
= 5050

(2^3)^8 * 2^(-2)^12* (-1)^12
=2^(3*8)* 2^(-24)*1
=1