{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" H\u00e3y ch\u1ecdn d\u1ea5u th\u00edch h\u1ee3p thay cho d\u1ea5u <span class='basic_hoi_black'>?<\/span> <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai7/lv3/img\/5.jpg' \/><\/center> <br\/> $625^{5}$ <span class='basic_hoi_black'>?<\/span> $125^{7}$","select":["A. >","B. < ","C. = "],"hint":"\u0110\u01b0a c\u1ea3 hai v\u1ebf v\u1ec1 c\u00f9ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 5 \u0111\u1ec3 so s\u00e1nh","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn: <br\/> <\/span> <b> PH\u01af\u01a0NG PH\u00c1P CHUNG: <\/b> <br\/> <i> Th\u01b0\u1eddng \u0111\u1ec3 so s\u00e1nh hai l\u0169y th\u1eeba ta \u0111\u01b0a v\u1ec1 d\u1ea1ng so s\u00e1nh hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 ho\u1eb7c c\u00f9ng s\u1ed1 m\u0169 <br\/> + N\u1ebfu hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1, l\u0169y th\u1eeba n\u00e0o c\u00f3 s\u1ed1 m\u0169 l\u1edbn h\u01a1n th\u00ec l\u1edbn h\u01a1n <br\/>N\u1ebfu m > n th\u00ec $a^m > a^n$ <br\/> + N\u1ebfu hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169 th\u00ec l\u0169y th\u1eeba n\u00e0o c\u00f3 c\u01a1 s\u1ed1 l\u1edbn h\u1edbn s\u1ebd l\u1edbn h\u01a1n <br\/> N\u1ebfu a > b th\u00ec $a^n > b^n$ <\/i> <br\/> <b> C\u1ee5 th\u1ec3: <\/b> Nh\u1eadn th\u1ea5y 625 v\u00e0 125 \u0111\u1ec1u l\u00e0 l\u0169y th\u1eeba c\u1ee7a 5 n\u00ean ta \u0111\u01b0a v\u1ec1 c\u00f9ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 5<br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u01b0a $625^{5}$ v\u00e0 $125^7$ v\u1ec1 l\u0169y th\u1eeba c\u01a1 s\u1ed1 5 b\u1eb1ng c\u00e1ch l\u1ea5y 625 v\u00e0 125 chia li\u00ean ti\u1ebfp cho 5 <br\/>$625 = 5^x$ n\u00ean $625^{5} = (5^x)^{5}= 5^{5x}$ <br\/> $125 = 5^a$ n\u00ean $125^7 =(5^a)^7 = 5^{7a}$ <br\/> <b> B\u01b0\u1edbc 2: <\/b> So s\u00e1nh $5^{5x}$ v\u00e0 $5^{7a}$ <br\/><br\/><\/span><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Nh\u1eadn th\u1ea5y 625 v\u00e0 125 \u0111\u1ec1u l\u00e0 c\u00e1c l\u0169y th\u1eeba c\u1ee7a 5 n\u00ean ta \u0111\u01b0a v\u1ec1 c\u00f9ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 5 \u0111\u1ec3 so s\u00e1nh<br\/> $625^{5} = (5 . 5 . 5 . 5)^{5} = (5^4)^5 = 5^{5.4} = 5^{20}$ <br\/>$125^7 = (5 . 5 . 5)^7 = (5^3)^7 = 5^{3.7} = 5^{21}$ <br\/> V\u00ec $5^{20} < 5^{21}$ <br\/> N\u00ean $625^{5} < 125^{7}$<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. < <\/span> <br\/> <span class='basic_green'> <i> L\u01b0u \u00fd: L\u0169y th\u1eeba c\u1ee7a m\u1ed9t t\u00edch b\u1eb1ng t\u00edch c\u00e1c l\u0169y th\u1eeba <br\/> $(a^m)^n = a^m.a^n (a \\neq 0; m,n \\in \\mathbb{n})$ <\/i><\/span> ","column":3}]}],"id_ques":341},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["2"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ecm x bi\u1ebft: <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai7/lv3/img\/4.jpg' \/><\/center> <br\/> $[(2x - 4)+9]^3 = 3^6$ <br\/> V\u1eady x = _input_","hint":"Bi\u1ebfn \u0111\u1ed5i VP v\u1ec1 l\u0169y th\u1eeba b\u1eadc 3 c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean sau \u0111\u00f3 cho 2 c\u01a1 s\u1ed1 b\u1eb1ng nhau \u0111\u1ec3 t\u00ecm x","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> PH\u01af\u01a0NG PH\u00c1P CHUNG: <\/b><br\/> <i> Ta bi\u1ebfn \u0111\u1ed5i bi\u1ec3u th\u1ee9c \u1edf hai v\u1ebf v\u1ec1 c\u00f9ng c\u01a1 s\u1ed1 ho\u1eb7c c\u00f9ng s\u1ed1 m\u0169 <br\/> +) N\u1ebfu VT v\u00e0 VP c\u00f3 c\u00f9ng c\u01a1 s\u1ed1 th\u00ec cho s\u1ed1 m\u0169 \u1edf 2 v\u1ebf b\u1eb1ng nhau \u0111\u1ec3 t\u00ecm x <br\/> ($a^x = a^y$ khi v\u00e0 ch\u1ec9 khi x = y)<br\/> +) N\u1ebfu VT v\u00e0 VP c\u00f3 c\u00f9ng s\u1ed1 m\u0169 th\u00ec ta cho c\u01a1 s\u1ed1 \u1edf 2 v\u1ebf b\u1eb1ng nhau r\u1ed3i t\u00ecm x <br\/> ($a^m = b^m$ khi v\u00e0 ch\u1ec9 khi a = b) <\/i> <br\/> <b> C\u1ee5 th\u1ec3: <\/b> <br\/><b> B\u01b0\u1edbc 1: <\/b> Bi\u1ebfn \u0111\u1ed5i $3^6$ v\u1ec1 l\u0169y th\u1eeba b\u1eadc 3 <br\/> <b> B\u01b0\u1edbc 2: <\/b> V\u00ec c\u1ea3 VP v\u00e0 VT \u0111\u1ec1u l\u00e0 l\u0169y th\u1eeba b\u1eadc 3 <br\/> Cho hai c\u01a1 s\u1ed1 b\u1eb1ng nhau \u0111\u1ec3 t\u00ecm x theo c\u00f4ng th\u1ee9c tr\u00ean<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $ \\begin{align*} \\text{Ta c\u00f3: } [(2x - 4)+9]^3 &= 3^6 \\\\ [(2x - 4)+9]^3 &= 3^{2.3} \\\\ [(2x - 4)+9]^3 &= (3^2)^3 \\\\ [(2x - 4)+9]^3 &= 9^3 \\end{align*}$ <br\/> $ \\begin{align*} \\text{Suy ra: } (2x - 4)+9 &= 9 \\\\ 2x - 4 + 9 &= 9 \\\\ 2x + 5 &= 9 \\\\ 2x &= 9 - 5 \\\\ x &= 2 \\end{align*}$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 2<\/span> <br\/> <span class='basic_green'> <i> L\u01b0u \u00fd: <\/i> $(a^m)^n = a^{m.n} (a \\neq 0; m, n \\in \\mathbb{N})$<\/span>"}]}],"id_ques":342},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["625"]]],"list":[{"point":10,"width":60,"type_input":"","ques":"T\u00ednh. <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai7/lv3/img\/2.jpg' \/><\/center> <br\/> $5^{10} . 25^4 . 125^2 : 625^5$ = _input_","hint":"Bi\u1ebfn \u0111\u1ed5i t\u1ea5t c\u1ea3 v\u1ec1 l\u0169y th\u1eeba c\u01a1 s\u1ed1 5 sau \u0111\u00f3 \u00e1p d\u1ee5ng quy t\u1eafc nh\u00e2n v\u00e0 chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> * Quy t\u1eafc: <\/b> <br\/> +) $a^m.a^n = a^{m + n}$ <br\/> +) $a^m:a^n = a^{m - n}$ <br\/> +) $a^m.b^m = (a.b)^n$ <br\/> +) $(a^m)^n = a^{m.n}$ <br\/> +) $a^m:b^m = (a: b)^m$ <br\/> V\u1edbi $a, b \\neq 0; m, n \\in \\mathbb{N}$ <br\/> <b> C\u1ee5 th\u1ec3: <\/b> <br\/> <b> B\u01b0\u1edbc 1: <\/b> Bi\u1ebfn \u0111\u1ed5i $25^4$, $125^2$; $625^5$ v\u1ec1 c\u00f9ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 5 <br\/> <b> B\u01b0\u1edbc 2: <\/b> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh nh\u00e2n v\u00e0 chia theo quy t\u1eafc nh\u00e2n, chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $ \\begin{align*} \\text{Ta c\u00f3: } & 5^{10} . 25^4 . 125^2 : 625^5 \\\\ =& 5^{10}. (5 . 5)^4 . (5 . 5 . 5)^2 : (5 . 5 . 5 . 5)^5 \\\\ =& 5^{10}. (5^2)^4 . (5^3)^2 : (5^4)^5 \\\\ =& 5^{10} . 5^8 . 5^6 : 5^{20} \\\\ =& 5^{10 + 8 + 6} : 5^{20} \\\\ =& 5^{24} : 5^{20} \\\\ =& 5^{24 - 20} \\\\ =& 5^4 \\\\ =& 625 \\end{align*}$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 625 <\/span> "}]}],"id_ques":343},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["12"]]],"list":[{"point":10,"width":60,"type_input":"","ques":"T\u00ednh. <br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai7/lv3/img\/2.jpg' \/><\/center> <br\/> $(3^{12} + 3^{11}) : 3^{10} $ = _input_","hint":"Nh\u00f3m $3^{10}$ \u1edf s\u1ed1 b\u1ecb chia ra l\u00e0m nh\u00e2n t\u1eed chung r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p chia","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> * Quy t\u1eafc: <\/b> <br\/> +) $a^m.a^n = a^{m + n}$ <br\/> +) $a^m:a^n = a^{m - n}$ <br\/> +) $a^m.b^m = (a.b)^n$ <br\/> +) $(a^m)^n = a^{m.n}$ <br\/> +) $a^m:b^m = (a: b)^m$ <br\/> V\u1edbi $a, b \\neq 0; m, n \\in \\mathbb{N}$ <br\/> <b> C\u1ee5 th\u1ec3: <\/b> <br\/> Nh\u1eadn th\u1ea5y \u1edf s\u1ed1 b\u1ecb chia c\u00f3 th\u1ec3 \u0111\u01b0a $3^{10}$ ra ngo\u00e0i l\u00e0m nh\u00e2n t\u1eed chung <br\/> <b> B\u01b0\u1edbc 1: <\/b> Nh\u00f3m $2^10$ ra ngo\u00e0i l\u00e0m nh\u00e2n t\u1eed chung <br\/> <b> B\u01b0\u1edbc 2: <\/b> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh chia $3^{10}. (....) : 3^{10} = ?$<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $ \\begin{align*} \\text{Ta c\u00f3: } & (3^{12} + 3^{11}) : 3^{10} \\\\ =& (3^{10 + 2} + 3^{10 + 1}) : 3^{10} \\\\ =& (3^{10}.3^2 + 3^{10}.3) : 3^{10} \\\\ =& 3^{10}.(3^2 + 3) : 3^{10} \\\\ =& 3^2 + 3 \\\\ =& 9 + 3 \\\\ =& 12 \\end{align*}$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 12 <\/span> "}]}],"id_ques":344},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai7/lv3/img\/10.jpg' \/><\/center> <br\/> $1048576 : 2^{12} = ?$ ","select":["A. $16^4$ ","B. $16^2$ ","C. $16^3$ "],"hint":"\u0110\u01b0a 1048576 v\u00e0 $2^{12}$ v\u1ec1 c\u00f9ng l\u0169y th\u1eeba c\u01a1 s\u1ed1 16 r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p chia","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn: <br\/> <\/span> <b> PH\u01af\u01a0NG PH\u00c1P CHUNG: <\/b> <br\/> <b> C\u00e1ch 1: <\/b> \u0110\u01b0a v\u1ec1 l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1ed1 r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh chia <br\/> $a^m : a^n = a^{m - n}$ <br\/> <b> C\u00e1ch 2: <\/b> \u0110\u01b0a v\u1ec1 l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169 r\u1ed3i th\u1ef1c hi\u1ec7n ph\u00e9p chia <br\/> $a^m : b^m = (a : b)^m$ <br\/> <b> C\u00e1ch 3: <\/b> T\u00ednh l\u0169y th\u1eeba r\u1ed3i th\u1ef1c hi\u1ec7n chia hai s\u1ed1 t\u1ef1 nhi\u00ean <br\/> (Kh\u00f4ng khuy\u1ebfn kh\u00edch v\u00ec ch\u1ec9 th\u1ef1c hi\u1ec7n \u0111\u01b0\u1ee3c v\u1edbi s\u1ed1 nh\u1ecf) <br\/> <b> C\u1ee5 th\u1ec3: <\/b> \u0110\u01b0a 1048576 v\u1ec1 l\u0169y th\u1eeba c\u01a1 s\u1ed1 16 b\u1eb1ng c\u00e1ch chia li\u00ean ti\u1ebfp cho 16 <br\/> \u0110\u01b0a $2^{12}$ v\u1ec1 l\u0169y th\u1eeba c\u01a1 s\u1ed1 16 b\u1eb1ng c\u00e1ch t\u00e1ch 12 = 4.3 (v\u00ec $2^4$ = 16) <br\/><br\/><\/span><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/> Ta c\u00f3: $1048576 = 16 . 16 . 16 . 16 . 16 = 16^5$ <br\/> $2^{12} = 2^{4 . 3} = (2^4)^3 = 16^3$ <br\/> N\u00ean $1048576 : 2^{12} = 16^5 : 16^3 = 16^{5 - 3} = 16^2$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0: B. $16^{2}$<\/span> ","column":3}]}],"id_ques":345},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" H\u00e3y \u0111i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai7/lv3/img\/5.jpg' \/><\/center> <br\/> $48^5 : 6^5$ _input_ $2^5 . 3^5$","hint":"\u00c1p d\u1ee5ng quy t\u1eafc nh\u00e2n v\u00e0 chia hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169 $a^m . b^m = (a. b)^m$; $a^m : b^m = (a: b)^m$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> * Quy t\u1eafc: <\/b> <br\/>+) $a^m:b^m = (a: b)^m$ <br\/> $a^m . b^m = (a. b)^m$<br\/> V\u1edbi $a, b \\neq 0; m, n \\in \\mathbb{N}$ <br\/> <b> C\u1ee5 th\u1ec3: <\/b> <br\/> <b> B\u01b0\u1edbc 1: <\/b> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh VP v\u00e0 VT <br\/> $48^5 : 6^5 = a^5$; $2^5 . 3^5 = b^5$<br\/> <b> B\u01b0\u1edbc 2: <\/b>So s\u00e1nh $a^5$ v\u1edbi $b^5$ v\u00e0 \u0111i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p <br\/> Khi so s\u00e1nh hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169, l\u0169y th\u1eeba n\u00e0o c\u00f3 c\u01a1 s\u1ed1 l\u1edbn h\u01a1n th\u00ec l\u1edbn h\u01a1n <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $48^5 : 6^5 = (48 : 6)^5 = 8^5$ <br\/> $2^5 . 3^5 = (2 . 3)^5 = 6^5$ <br\/> M\u00e0 $8^5 > 6^5$ n\u00ean $48^5 : 6^5 > 2^5 . 3^5$ <br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0: > <\/span> "}]}],"id_ques":346},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":10,"width":60,"type_input":"","ques":" H\u00e3y \u0111i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop6/toan/daiso/bai7/lv3/img\/5.jpg' \/><\/center> <br\/> $1001^8 : 7^8$ _input_ $7^8 . 11^8$","hint":"\u00c1p d\u1ee5ng quy t\u1eafc nh\u00e2n v\u00e0 chia hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169 $a^m . b^m = (a.b)^m$; $a^m : b^m = (a: b)^m$","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> * Quy t\u1eafc: <\/b> <br\/> +) $a^m:b^m = (a: b)^m$ <br\/> $a^m . b^m = (a.b)^m$ <br\/> V\u1edbi $a, b \\neq 0; m, n \\in \\mathbb{N}$ <br\/> <b> C\u1ee5 th\u1ec3: <\/b> <br\/> <b> B\u01b0\u1edbc 1: <\/b> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh \u1edf VP v\u00e0 VT <br\/> $1001^8 : 7^8 = a^8$ ; $7^8 . 11^8 = b^8$ <br\/> <b> B\u01b0\u1edbc 2: <\/b>So s\u00e1nh $a^8$ v\u00e0 $b^8$ v\u00e0 \u0111i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p <br\/> Khi so s\u00e1nh hai l\u0169y th\u1eeba c\u00f9ng s\u1ed1 m\u0169, l\u0169y th\u1eeba n\u00e0o c\u00f3 c\u01a1 s\u1ed1 l\u1edbn h\u01a1n th\u00ec l\u1edbn h\u01a1n <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $1001^8 : 7^8 = (1001 : 7)^8 = 143^8$ <br\/> $7^8 . 11^8 = (7 . 11)^8 = 77^8$ <br\/> M\u00e0 $143^8 > 77^8$ n\u00ean $1001^8 : 7^8$ > $37^8 . 11^8$ <br\/> <span class='basic_pink'>V\u1eady d\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0: > <\/span> "}]}],"id_ques":347},{"time":14,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["620"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["sqr"],"ques":"H\u00e3y vi\u1ebft t\u00edch sau d\u01b0\u1edbi d\u1ea1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean: <br\/> 22 . 24 . 26 . 28 + 16 = _input_<sup>2<\/sup>","hint":"T\u00ednh k\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p t\u00ednh tr\u00ean r\u1ed3i bi\u1ebfn \u0111\u1ed5i k\u1ebft qu\u1ea3 th\u00e0nh d\u1ea1ng l\u0169y th\u1eeba b\u1eadc 2 c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00ednh 22 . 24 . 26 . 28 + 16 = ? <br\/> <b> B\u01b0\u1edbc 2: <\/b> Bi\u1ebfn \u0111\u1ed5i k\u1ebft qu\u1ea3 b\u01b0\u1edbc 1 th\u00e0nh d\u1ea1ng l\u0169y th\u1eeba b\u1eadc 2 c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> 22 . 24 . 26 . 28 + 16 = 384384 + 16 = 384400 <br\/> $384400 = 3844 . 100 = 961 . 4 . 10^2 = 31^2 . 2^2 . 10^2 = (31 . 2 . 10)^2 = 620^2$ <br\/> V\u1eady t\u00edch $22 . 24 . 26 . 28 + 16 = 620^2$ <br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 620 <\/span> <br\/> <span class='basic_green'> <i> Nh\u1eadn x\u00e9t: T\u00edch b\u1ed1n s\u1ed1 ch\u1eb5n li\u00ean ti\u1ebfp c\u1ed9ng 16 lu\u00f4n vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean<\/i> <\/span>"}]}],"id_ques":348},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["32"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ednh. <br\/> $\\dfrac{2^{23} + 2^{24} + 2^{25}}{2^{18} + 2^{19} + 2^{20}}$ = _input_","hint":"Nh\u00f3m nh\u00e2n t\u1eed chung \u1edf t\u1eed v\u00e0 nh\u00e2n t\u1eed chung \u1edf m\u1eabu r\u1ed3i r\u00fat g\u1ecdn","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Nh\u00f3m $2^{18}$ \u1edf t\u1eed s\u1ed1 l\u00e0m nh\u00e2n t\u1eed chung <br\/> <b> B\u01b0\u1edbc 2: <\/b> Nh\u00f3m $2^{18}$ \u1edf m\u1eabu l\u00e0m nh\u00e2n t\u1eed chung <br\/> <b> B\u01b0\u1edbc 3: <\/b> R\u00fat g\u1ecdn $2^{18}$ \u1edf t\u1eed v\u00e0 m\u1eabu r\u1ed3i t\u00ednh<\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: <br\/> $\\begin{align*} & \\dfrac{2^{23} + 2^{24} + 2^{25}}{2^{18} + 2^{19} + 2^{20}} \\\\ =& \\dfrac{2^{18 + 5} + 2^{18 + 6} + 2^{18 + 7} }{2^{18} + 2^{18 + 1} + 2^{18 + 2}} \\\\ =& \\dfrac{2^{18}.2^5 + 2^{18} . 2^6 + 2^{18} . 2^7}{2^{18} + 2^{18}.2 + 2^{18}.2^2} \\\\ =& \\dfrac{2^{18}. (2^5 + 2^6 + 2^7)}{2^{18}. (1 + 2 + 2^2)} \\\\ =& \\dfrac{32 + 64 + 128}{1 + 2 + 4} \\\\ =& \\dfrac{224}{7} \\\\ =& 32 \\end{align*}$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 32 <\/span> "}]}],"id_ques":349},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["8"]]],"list":[{"point":10,"width":50,"type_input":"","ques":"T\u00ednh. <br\/> $\\dfrac{72^3 . 54^2}{108^4}$ = _input_","hint":"108 = 54 . 2 n\u00ean ta bi\u1ebfn \u0111\u1ed5i $108^4 = 54^2.a$ r\u1ed3i r\u00fat g\u1ecdn v\u1edbi $54^2$ \u1edf t\u1eed","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> Nh\u1eadn th\u1ea5y 108 = 54.2 n\u00ean: <br\/> <b> B\u01b0\u1edbc 1: <\/b> Bi\u1ebfn \u0111\u1ed5i $108^4 = 54^2 . a$ r\u1ed3i r\u00fat g\u1ecdn v\u1edbi $54^2$ \u1edf t\u1eed s\u1ed1 <br\/> <b> B\u01b0\u1edbc 2: <\/b> 72 v\u00e0 54 c\u00f9ng chia h\u1ebft cho 18 n\u00ean ta bi\u1ebfn \u0111\u1ed5i t\u1eed s\u1ed1 v\u00e0 m\u1eabu s\u1ed1 v\u1ec1 c\u01a1 s\u1ed1 18 \u0111\u1ec3 r\u00fat g\u1ecdn <\/span> <br\/><br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> $\\begin{align*} & \\dfrac{72^3 . 54^2}{108^4} \\\\ =& \\dfrac{72^3 . 54^2}{(54.2)^4} \\\\ =& \\dfrac{72^3 . 54^2}{54^4 . 2^4} \\\\ =& \\dfrac{(18.4)^3}{54^2 . 2^4} \\\\ =& \\dfrac{18^3. 4^3}{(18 . 3)^2 . (2^2)^2} \\\\ =& \\dfrac{18^3 . 4^3}{18^2 . 3^2 . 4^2} \\\\ =& \\dfrac{18 . 4}{3^2} \\\\ =& \\frac{72}{9} \\\\ =& 8 \\end{align*}$ <br\/> <span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0: 8 <\/span> "}]}],"id_ques":350}],"lesson":{"save":0,"level":3}}