Verification: the 13th power of 81 7th power - 27 9th power - 9 can be divided by 45

Verification: the 13th power of 81 7th power - 27 9th power - 9 can be divided by 45

Proof: ∵ 81 ^ 7-27 ^ 9-9 ^ 13 = (9 * 9) ^ 7 - (9 * 3) ^ 9-9 ^ 13
=9^7*9^7-9^9*3^9-9^13
=9^9(9^5-3^9-9^4)
=9^9(3^5*3^5-3^9-3^4*3^4)
=9^9*3^8(3^2-3-1)
=9^9*3^8*5
=9*9^8*3^8*5
=45*9^8*3^8
The 13th power of 81 to the seventh power - 27 to the ninth power - 9 can be divided by 45

Try to explain: the seventh power of 81 minus the ninth power of 27 minus the thirteenth power of 9 can be divided by 45;

81^7-27^9-9^13
=(3^4)^7-(3^3)^9-(3^2)^13
=3^28-3^27-3^26
=3^26*(3^2-3^1-1)
=3^24*3^2*(9-3-1)
=3^24*9*5
=3^24*45
The result must be an integral multiple of 45 and can be divided by 45

The 2008 derivative of x times e to the power of X

Available higher derivative formulas:
2008 derivative of (Xe ^ x)
=X * (2008 derivative of e ^ x) + 2008 * x '* (2007 derivative of e ^ x)
=xe^x+2008e^x
=(x+2008)e^x

If the power 0 of (3x + 2y-10) is meaningless and 2x + y = 5, find the values of X and y

According to the meaning of the topic:
3x+2y-10=0
2x+y=5
therefore
y=5-2x
Substitute the above formula to obtain:
3x+2*(5-2x)=10
10-x=10
x=0
y=5

Given that the x power of 2 = A and the Y power of 2 = B, find the X + y power of 2 + the 3x + 2Y power of 2

2^(x+y)+2^(3x+2y)
=2^x × 2^y+2^3x × 2^2y
=2^x × 2^y+(2^x) ³× (2^y) ², Substitute 2 ^ x = A and 2 ^ y = B
=a × b+a ³× b ²
=ab+a ³ b ²

(Y-5) to the power of 0 = 1 is meaningless, and 3x + 2Y = 10, find the values of X and y Thank you!

Meaningless, so Y-5 = 0, so y = 5, substituted into the following formula, so x = 0