Compare 3 to the power of 555, 4 to the power of 444, and 5 to the power of 333 to be a little more

That's 111 times for 243, 111 times for 256, and 111 times for 125.

Got it.

333The relationship between the three is 4 444 3 555 5 333.

Solution: Since 333=(5 3) 111, then to compare the size of 333, you only need to compare the size of 3 5, 4 4 and 5 3.

And 3 5 = 243, 4 4 = 256, 5 3 = 125, then.

4 4 = 256 3 5 = 243 5 3 = 125, so 4 444 3 555 5 333.

Extended information: Algorithms for power operations.

1. The multiplication method of power is: the base number is unchanged, and the exponents are multiplied.

Example: (x 3) 3=x (3*3)=x 9

2. Multiplication rule of the same base power: the base does not change, and the exponents are added.

Example: x 4*x 5=x (4+5)=x 9

x^3*y^5*x^8*y^4=x^(3+8)*y^(5+4)=x^11*y^9

3. The division rule of the same base power: the base does not change, and the exponent is subtracted.

Example: x 12 x 7 = x (12-7) = x 5

x^11*y^13÷(x^8*y^4)=x^(11-8)*y^(13-4)=x^3*y^9

3 555 = (Tomb 3 5) 111 = 243 111

Because: 256> ulnar cavity fluid 243>125

So: 4 444 > 3 555> 5 333

Hello: 2 to the 555th power = (2 to the 5th power) to the 111th power of the servant = 32 to the 111th power of 3 to the 444th power = (3 to the 4th power) to the 111th power = 81 to the 111th power of 4 to the 333rd power of the 4 = (4 to the 3rd power) to the 111th power = 64 to the 111th power so the loss of the Qing 3 to the 444th power of the 4 to the 333rd power of the 4 to the 555th power of the 2 If you approve of me, please catch.

3 to the 555th power = (3 to the 5th power) to the 111th power = 243 to the 111th power of Okiga.

4 to the power of 4 = (4 to the power of 4) to the power of 111 = 256 to the power of 111.

5 to the power of 333 = (5 to the power of 3) to the power of 111 = 125 to the power of 111.

4 to the power of 4, to the power of 555 greater than 3, to the power of 3, to the power of 333 to the power of 5.

I, 3 555 = (3 5) 111, 4 444 = (4 4) 111, 5 333 = (5 3) 111;

two, 3 5 = 243, 4 4 = 256, 5 3 = 125;

Third, from the small core or the change to the large platoon group Huilie: 5 333, 3 555, 4 444

a=3^555=(3^5)^111

b=4^444=(4^4)^111

c=5^333=(5^3)^111

So. Just compare the size of 3.

And these three numbers can be calculated by Feng Fu.

Because 5 3< 3 5 "Hall is 4 4

So C "Silver Troy A

3 to the power of 555 = (3 to the power of 5) to the power of 111 = 243 to the power of 111 = 4 to the power of 4 to the power of 4 = (4 to the power of 4) to the power of 111 = 64 to the power of 111 = 3 to the power of 5 to the power of 5 = 111 to the power of 125, so 3 to the power of 5 to the power of 444 to the power of 4 to the 333rd power I hope to adopt, thank you.

It is the size relationship between 3 and 5, 4 and 5.

333The relationship between the three is 4 444 3 555 5 333.

Solution: Since 333=(5 3) 111, then to compare the size of 333, you only need to compare the size of 3 5, 4 4 and 5 3.

And 3 5 = 243, 4 4 = 256, 5 3 = 125, then.

4 4 = 256 3 5 = 243 5 3 = 125, so 4 444 3 555 5 333.

Extended information: Algorithms for power operations.

1. The multiplication method of power is: the base number is unchanged, and the exponents are multiplied.

Example: (x 3) 3=x (3*3)=x 9

2. Multiplication rule of the same base power: the base does not change, and the exponents are added.

Example: x 4*x 5=x (4+5)=x 9

x^3*y^5*x^8*y^4=x^(3+8)*y^(5+4)=x^11*y^9

3. The division rule of the same base power: the base does not change, and the exponent is subtracted.

Example: x 12 x 7 = x (12-7) = x 5

x^11*y^13÷(x^8*y^4)=x^(11-8)*y^(13-4)=x^3*y^9