Determine the last 3 digits of 999^999

the last three digits are 999

Step-by-step explanation:

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