Compare the size of the 100th power of 2 with the 75th power of 3?

Compare the size of the 100th power of 2 with the 75th power of 3?

126750600228229401496703205376 this is the 100th power of 2
2^100=(2^4)^25=16^25
3^75=(3^3)^25=27^25
Because: the 25th power of 16 is less than the 25th power of 27
So: 3 ^ 75 is greater than 2 ^ 100

Try to compare the size of the 100th power of 2 with the 75th power of 3 It is only the 100th power of 2 = (the 4th power of 2) the 25th power of 16, and the 75th power of 3 = (3) ³） The 25th power of = the 25th power of 27 and 16 < 27, so the 100th power of 2 < the 75th power of 3 Compare the size of the 55th power of 2, the 44th power of 3 and the 33rd power of 4

The 100th power of 2 = (2 ^ 4) ^ 25 = the 25th power of 16
The 75th power of 3 = (3 ^ 3) ^ 25 = the 25th power of 27
The 25th power of 16 and the 55th power of 2

How big is the 100th power of 2 compared with the 75th power of 3? What kind of thinking

100th power of 2 = (4th power of 2) 25th power = 25th power of 16
75th power of 3 = (3rd power of 3) 25th power = 25th power of 27
Obviously, the 75th power of 3 is larger

Some people say that when n is a positive integer, the nth power of 1 is equal to 1, and the nth power of (- 1) is also equal to 1, 1. Some people say that when n is a positive integer, the nth power of 1 is equal to 1, and the nth power of (- 1) is also equal to 1. Why? 2. Can you find the positive integer n satisfying the nth power of (n-3) = (n-3) to the 2n-2 power? 3. Can you find the positive integer n satisfying the N + 3 power of (n-3) = (n-3) to the 2n power?

1. Some people say that when n is a positive integer, the nth power of 1 is equal to 1, right
The nth power of (- 1) is also equal to 1, and the power of error (- 1) is also equal to - 1
2. You can find the positive integer n satisfying the nth power of (n-3) = (n-3) to the 2n-2 power
N = 2n-2 n = 2 energy
3. You can find the positive integer n satisfying the N + 3rd power of (n-3) = (n-3) to the 2nth power
N + 3 = 2n, n = 3 (n-3) ≠ 0, so it cannot be

Why is the zeroth power of n (positive integer) equal to 1

1. Division rule of the power of the same base
Am ÷ an = the (m-n) power of a (a ≠ 0, m and N are positive integers, M > n)
Divide by the power of the base, the base remains unchanged, and the exponent is subtracted
2. In the law, if M = n, there is a zero exponent a to the power of 0 = 1 (a ≠ 0)
The zeroth power of any number that is not equal to 0 is equal to 1
3. In the rule, if M < n, there is a negative integer exponent a to the - P power = (a ≠ 0, P is a positive integer)
The - P power of any number not equal to 0 (P is a positive integer) is equal to the reciprocal of the P power of the number

The square of x equals 64. What is x? The third power of x equals 64. What is x?

The square of x equals 64
X = ± root sign (64)
x=±8
The third power of X is 64,
X = 3rd root sign (64)
x=4