^=to the power
in Other Math Topics by Level 4 User (7.9k points)

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last 3 digits=999
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I thought it was wrong or a joke or something, but it's right.

Any digits after the 100s place won't affect anything in the 100s, 10s, or 1s places, so the question is the same as asking about the last 3 digits of 999^999

999^999 = 368 063 488 259 223 267 894 700 840 060 521 865 838 338 232 037 353 204 655 959 621 437 025 609 300 472 231 530 103 873 614 505 175 218 691 345 257 589 896 391 130 393 189 447 969 771 645 832 382 192 366 076 536 631 132 001 776 175 977 932 178 658 703 660 778 465 765 811 830 827 876 982 014 124 022 948 671 975 678 131 724 958 064 427 949 902 810 498 973 271 030 787 716 781 467 419 524 180 040 734 398 996 952 930 832 508 934 116 945 966 120 176 735 120 823 151 959 779 536 852 290 090 377 452 502 236 990 839 453 416 790 640 456 116 471 139 751 546 750 048 602 189 291 028 640 970 574 762 600 185 950 226 138 244 530 187 489 211 615 864 021 135 312 077 912 018 844 630 780 307 462 205 252 807 737 757 672 094 320 692 373 101 032 517 459 518 497 524 015 120 165 166 724 189 816 766 397 247 824 175 394 802 028 228 160 027 100 623 998 873 667 435 799 073 054 618 906 855 460 488 351 426 611 310 634 023 489 044 291 860 510 352 301 912 426 608 488 807 462 312 126 590 206 830 413 782 664 554 260 411 266 378 866 626 653 755 763 627 796 569 082 931 785 645 600 816 236 891 168 141 774 993 267 488 171 702 172 191 072 731 069 216 881 668 294 625 679 492 696 148 976 999 868 715 671 440 874 206 427 212 056 717 373 099 639 711 168 901 197 440 416 590 226 524 192 782 842 896 415 414 611 688 187 391 232 048 327 738 965 820 265 934 093 108 172 054 875 188 246 591 760 877 131 657 895 633 586 576 611 857 277 011 782 497 943 522 945 011 248 430 439 201 297 015 119 468 730 712 364 007 639 373 910 811 953 430 309 476 832 453 230 123 996 750 235 710 787 086 641 070 310 288 725 389 595 138 936 784 715 274 150 426 495 416 196 669 832 679 980 253 436 807 864 187 160 054 589 045 664 027 158 817 958 549 374 490 512 399 055 448 819 148 487 049 363 674 611 664 609 890 030 088 549 591 992 466 360 050 042 566 270 348 330 911 795 487 647 045 949 301 286 614 658 650 071 299 695 652 245 266 080 672 989 921 799 342 509 291 635 330 827 874 264 789 587 306 974 472 327 718 704 306 352 445 925 996 155 619 153 783 913 237 212 716 010 410 294 999 877 569 745 287 353 422 903 443 387 562 746 452 522 860 420 416 689 019 732 913 798 073 773 281 533 570 910 205 207 767 157 128 174 184 873 357 050 830 752 777 900 041 943 256 738 499 067 821 488 421 053 870 869 022 738 698 816 059 810 579 221 002 560 882 999 884 763 252 161 747 566 893 835 178 558 961 142 349 304 466 506 402 373 556 318 707 175 710 866 983 035 313 122 068 321 102 457 824 112 014 969 387 225 476 259 342 872 866 363 550 383 840 720 010 832 906 695 360 553 556 647 545 295 849 966 279 980 830 561 242 960 013 654 529 514 995 113 584 909 050 813 015 198 928 283 202 189 194 615 501 403 435 553 060 147 713 139 766 323 195 743 324 848 047 347 575 473 228 198 492 343 231 496 580 885 057 330 510 949 058 490 527 738 662 697 480 293 583 612 233 134 502 078 182 014 347 192 522 391 449 087 738 579 081 585 795 613 547 198 599 661 273 567 662 441 490 401 862 839 817 822 686 573 112 998 663 038 868 314 974 259 766 039 340 894 024 308 383 451 039 874 674 061 160 538 242 392 803 580 758 232 755 749 310 843 694 194 787 991 556 647 907 091 849 600 704 712 003 371 103 926 967 137 408 125 713 631 396 699 343 733 288 014 254 084 819 379 380 555 174 777 020 843 568 689 927 348 949 484 201 042 595 271 932 630 685 747 613 835 385 434 424 807 024 615 161 848 223 715 989 797 178 155 169 951 121 052 285 149 157 137 697 718 850 449 708 843 330 475 301 440 373 094 611 119 631 361 702 936 342 263 219 382 793 996 895 988 331 701 890 693 689 862 459 020 775 599 439 506 870 005 130 750 427 949 747 071 390 095 256 759 203 426 671 803 377 068 109 744 629 909 769 176 319 526 837 824 364 926 844 730 545 524 646 494 321 826 241 925 107 158 040 561 607 706 364 484 910 978 348 669 388 142 016 838 792 902 926 158 979 355 432 483 611 517 588 605 967 745 393 958 061 959 024 834 251 565 197 963 477 521 095 821 435 651 996 730 128 376 734 574 843 289 089 682 710 350 244 222 290 017 891 280 419 782 767 803 785 277 960 834 729 869 249 991 658 417 000 499 998 999

So yeah, 999.
Series
9999999^2=99999980000001
Again 9999999^3=...............999
Again 9999999^4=...............001
Again 9999999^5=...............999
Thus When power is odd last three digits are 999 and when even it is 001
Thanks.  That's a better, more general answer.

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