Calculation: how much is the sum of 2 to the power of 2007 plus 2 to the power of 2007 divided by 7?

Calculation: how much is the sum of 2 to the power of 2007 plus 2 to the power of 2007 divided by 7?

2007 power of 2 = 669 power of 8 divided by 7 (any power of 8 is divided by 7)
The second power of 2007 is divided by 7, the remainder of 5 is divided by 7, the remainder of 4 is divided by 7
Add up = 5

What's the 139th power of 38 divided by 11? What's the 131st power of 29 divided by 11?

As long as the problem is to master the method, it will be very simple
Let me show you first, 38 ^ 139 / 11 = 38 * 38 ^ 138 / 11 = (33 + 5) * 38 ^ 138 / 11
So (33 + 5) * 38 ^ 138 = 5 * 38 ^ 138 (mod11), I don't know Baidu. That is to say, (33 + 5) * 38 ^ 138 is divided into two parts, one part can be divided by 11, and the rest is what we should pay attention to
Then 5 ^ 139 = 5 * 25 ^ (138 / 2) = 5 * 25 ^ 69. Further decompose it into 5 * 25 ^ 69 = 5 * (22 + 3) ^ 69, and then remove the part with the factor 11, which is 5 * 3 ^ 69. Further simplify it into 5 * 27 ^ 23 = 5 * 5 ^ 23 = 5 ^ 24 = 25 ^ 12 = 3 ^ 12 = 27 ^ 4 = 5 ^ 4 = 25 ^ 2 = 3 ^ 2 = 9 (mod11)
Thinking should be very clear, as long as there is a multiple of 11 as the number of factors, divided by 11, the remainder is 0. Try to do the following one, do not understand

(the fifth power of X + the fourth power of X + the square of 5x + 5x + 6) divided by (the square of X + X + 1) divided by (x + 2)

(the fifth power of X + the fourth power of X + the square of 5x + 5x + 6) divided by (the square of X + X + 1) divided by (x + 2)
=(the 5th power of X + the 4th power of X + the 3rd power of X - the 3rd power of X - the square of X - x + the square of 6x + 6x + 6) divided by (the square of X + X + 1) divided by (x + 2)
=[x³(x²＋x＋1)-x(x²＋x＋1)+6(x²＋x＋1)÷(x²＋x＋1)÷(x+2)
=(x²＋x＋1)(x³-x+6)÷(x²＋x＋1)÷(x+2)
=(x³-x+6)÷(x+2)
=（x³＋2x²-2x²-4x＋3x＋6）÷(x+2)
=[x²(x+2)-2x(x+2)+3(x+2)]÷(x+2)
=(x+2)(x²-2x+3)÷(x+2)
=x²-2x+3

108 divided by the power of (- 2) - (- 1)
-The power of 10 + 8 divided by (- 2) - (- 1) is wrong

108 divided by the power of (- 2) - (- 1)
=108÷4-（-1）
=27+1
=28

A math problem: if X: Y: z = 2:3:4, find the value of fraction X-Y-Z / 2x + 3Y
If X: Y: z = 2:3:4, find the value of fraction X-Y-Z / 2x + 3Y

Let x = 2A, y = 3A, z = 4A,
So X-Y-Z / 2x + 3Y = (- 5A) / (13a) = - 5 / 13

2x+3Y=-5 x+3y=-7 x-y=3

2x+3Y=-5 ①
x+3y=-7 ②
x-y=3 ③
②- ③ 4y=-10 y=-2.5
Take y = - 2.5 into 3 to get x = 0.5
Take x = 0.5 into ① to get y = - 2

2X ^ 2 + 3Y ^ 2-8x + 6y + 11 = 0 for x + y=

Formula: 2 (X-2) ^ 2 + 3 (y + 1) ^ 2 = 0
If the sum of two nonnegative numbers is 0, they are both 0
So X-2 = 0
y+1=0
So x = 2
y=-1
x+y=1

Given the equation system x + y = 3A + 9 2x-3y = 11a-2, and X-Y = 6, find the value of A

x+y=3a+9 （1）
2x-3y=11a-2（2）
x-y=6（3）
This is a system of linear equations with three variables
(1) + (3) get, 2x = 3A + 15 (4)
(1) * 3 + (2) get: 3x + 2x = 9A + 11a + 27-2, sort out x = 4A + 5 (5) into (4)
8a+10=3a+15
5a=5
a=1

The sixth power of (X-Y) × (Y-X) the fifth power of (X-Y) × (X-Y) the fourth power of (X-Y)

The sixth power of (X-Y) × (Y-X) the fifth power of (X-Y) × (X-Y) the fourth power of (X-Y)
=The sixth power of (Y-X) × (Y-X) the fifth power of (Y-X) × (Y-X) the fourth power of (Y-X)
=(6 + 5 + 4) power of (Y-X)
=The 15th power of (Y-X)

Merge similar terms: 2n power of (X-Y) minus 2n power of (Y-X)
N is an integer

The 2nth power of (X-Y) minus the 2nth power of (Y-X)
=2n power of (X-Y) - (X-Y)
=0