Toán CM `24^54`.`54^24`.`2^10`chia hết cho`72^63` 20/07/2021 By Vivian CM `24^54`.`54^24`.`2^10`chia hết cho`72^63`
Đáp án+Giải thích các bước giải: `24^{54}.54^{24}.2^{10}` `=(3.8)^{54}.(27.2)^{24}.2^{10}` `=3^{54}.8^{54}.2^{24}.27^{24}.2^{10}` `=3^{54}.2^{34}.8^{54}.27^{24}` `=3^{54}.2^{34}.2^{162}.3^{72}` `=3^{126}.2^{196}` `=(3^{3})^{63}.2^{189}.2^{7}` `=9^{63}.(2^{3})^{63}.2^{7}` `=9^{63}.8^{63}.2^7` `=2^{7}.(8.9)^{63}` `=2^{7}.72^{63} vdots 72^{63}` Trả lời
Đáp án: Ta có : `24^{54} . 54^{24} . 2^{10}` `= (3.8)^{54} .(27 . 2)^{24} . 2^{10}` `= 3^{54} . 8^{54} . 27^{24} . 2^{24} . 2^{10}` `= 3^{54} . (2^3)^{54} . (3^3)^{24} . 2^{24} . 2^{10}` ` = 3^{54} . 2^{162} . 3^{72} . 2^{24} . 2^{10}` `= 2^{196} . 3^{126}` `= 2^7 . 2^{189} . 3^{126}` `= 2^7 . 8^{63} . 9^{63}` `= 2^7 . 72^{63}` chia hết cho` 72^{63}` Giải thích các bước giải: Trả lời
Đáp án+Giải thích các bước giải:
`24^{54}.54^{24}.2^{10}`
`=(3.8)^{54}.(27.2)^{24}.2^{10}`
`=3^{54}.8^{54}.2^{24}.27^{24}.2^{10}`
`=3^{54}.2^{34}.8^{54}.27^{24}`
`=3^{54}.2^{34}.2^{162}.3^{72}`
`=3^{126}.2^{196}`
`=(3^{3})^{63}.2^{189}.2^{7}`
`=9^{63}.(2^{3})^{63}.2^{7}`
`=9^{63}.8^{63}.2^7`
`=2^{7}.(8.9)^{63}`
`=2^{7}.72^{63} vdots 72^{63}`
Đáp án:
Ta có :
`24^{54} . 54^{24} . 2^{10}`
`= (3.8)^{54} .(27 . 2)^{24} . 2^{10}`
`= 3^{54} . 8^{54} . 27^{24} . 2^{24} . 2^{10}`
`= 3^{54} . (2^3)^{54} . (3^3)^{24} . 2^{24} . 2^{10}`
` = 3^{54} . 2^{162} . 3^{72} . 2^{24} . 2^{10}`
`= 2^{196} . 3^{126}`
`= 2^7 . 2^{189} . 3^{126}`
`= 2^7 . 8^{63} . 9^{63}`
`= 2^7 . 72^{63}` chia hết cho` 72^{63}`
Giải thích các bước giải: