(- 2) 50th power + (- 2) 49th power + (- 2) 48th power +. + (- 2) + 1 thank you.

(- 2) 50th power + (- 2) 49th power + (- 2) 48th power +. + (- 2) + 1 thank you.

(-2)^50+(-2)^49+(-2)^48+…+(-2)+1
=2^50-2^49+2^48-2^47+...-2+1,
=2*2^49-2^49+2*2^47-2^47+...-1
=2^49+2^47+...+2+1
Let B = 2 ^ 49 + 2 ^ 47 +... + 2 + 1,
So 4B = 2 ^ 51 + 2 ^ 49 +... + 2 ^ 3 + 4,
So 4b-b = 2 ^ 51 + 1,
So 3B = 2 ^ 51 + 1,
So B = (2 ^ 51 + 1) / 3,
That is (- 2) ^ 50 + (- 2) ^ 49 + (- 2) ^ 48 +... + (- 2) + 1 = (2 ^ 51 + 1) / 3

The solution of the 50th power of (- 2) + the 49th power of (- 2) + the 48th power of (- 2)... + (- 2) + 1

(- 2) to the 50th power + (- 2) to the 49th power + (- 2) to the 48th power... + (- 2) + 1
=((- 2) to the 51st power - 1) / (- 2-1) = (2 to the 51st power + 1) / 3

The result of calculating (- 2) 50th power + (- 2) 51st power is

(- 2) 50th power + (- 2) 51st power. Er. Power. You can use ^ as the symbol
∵ (- 2) ^ 51 = - (- 2) ^ 50 * 2 = - {(- 2) ^ 50 + (- 2) ^ 50} (the odd power of a negative number is a negative number)
∴（-2）^50+(-2)^51=-{(-2)^50+(-2)^50}+(-2)^50=-(-2)^50
It can also be written as - 2 ^ 50, (recommended)

Can the 7th power of 81 minus the 9th power of 27 minus the 13th power of 9 be divided by 45?

can
The 7th power of 81 = the 28th power of 3
The 9th power of 27 = the 27th power of 3
The 13th power of 9 = the 26th power of 3
That is, 3 ^ 28-3 ^ 27-3 ^ 26 = 2 * 3 ^ 27-3 ^ 26 = 5 * 3 ^ 26 = 45 * 3 ^ 24

Verification: 817-279-913 can be divided by 45

Proof: original formula = 914-99 × 39-913
=328-327-326
=326（32-3-1）
=326 × five
=324 × thirty-two × five
=45 × 324．
So it can be divided by 45

Verification: 817-279-913 can be divided by 45

Proof: original formula = 914-99 × 39-913
=328-327-326
=326（32-3-1）
=326 × five
=324 × thirty-two × five
=45 × 324．
So it can be divided by 45