Amazing Power Relationship

Our number system has many unusual features built into it. Here is one of them discovered by Carl Friedrich Gauss (1777 – 1855).

81 = (8+1)² = 9² 
or 4,193 = (4+1+9+3)³ = 17³

Now enjoy the list.

81 = 9²

512 = 8³

4,193 = 17³

5,832 = 18³

17,576 = 26³

19,683 = 27³

2,401 = 7⁴

234,256 = 22⁴

390,625 = 25⁴

614,656 = 28⁴

1,679,616 = 36⁴

17,210,368 = 28⁵

52,521,875 = 35⁵

60,466,176 = 36⁵

205,962,976 = 46⁵

34,012,224 = 18⁶

8,303,765,625 = 45⁶

24,794,911,296 = 54⁶

68,719,476,736 =64⁶

612,220,032 = 18⁷

10,460,353,203 = 27⁷

27,512,614,111 = 31⁷

52,523,350,144 = 34⁷

271,818,611,107 = 43⁷

1,174,711,139,837 = 53⁷

2,207,984,167,552 = 58⁷

6,722,988,818,432 = 68⁷

20,047,612,231,936 = 46⁸

72,301,961,339,136 = 54⁸

248,155,780,267,521 = 63⁸

20,864,448,472,975,628,947,226,005,981,267,194,447,042,584,001 = 207²⁰