a) \(512:2^5\)
b) \(\left(\frac{16}{81}\right)^3\)\(:\left(\frac{4}{9}\right)^2\)
c) \(\left(-\frac{1}{2}\right)^3\)\(:\left(\frac{-1}{2^{ }}\right)^2\)
d) \(256:2^4\)
giải giúp tui, trước 6h tối nay, cậu nào đúng thì tui T I C K:))
Tìm số nguyên N biết:
\(a,\left(\frac{1}{3}\right)^n=\frac{1}{81}\)
\(b,\frac{-512}{343}=\left(\frac{-8}{7}\right)^n\)
\(c,\left(\frac{-3}{4}\right)^n=\frac{81}{256}\)
\(d,\left(2x+3\right)^2=\frac{9}{121}^n\)
a) \(\left(\frac{1}{3}\right)^n=\frac{1}{81}\)
\(\Rightarrow\left(\frac{1}{3}\right)^n=\frac{1^4}{3^4}\)
\(\Rightarrow\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^4\)
\(\Rightarrow n=4\)
Vậy n = 4
b) \(\frac{-512}{343}=\left(\frac{-8}{7}\right)^n\)
\(\Rightarrow\frac{-8^3}{7^3}=\left(\frac{-8}{7}\right)^n\)
\(\Rightarrow\left(\frac{-8}{7}\right)^3=\left(\frac{-8}{7}\right)^n\)
\(\Rightarrow n=3\)
Vậy n = 3
Giúp mik với
Tính
a)\(\frac{2}{3}\sqrt{81}-\left(\frac{-3}{4}\right).\sqrt{\frac{9}{64}}+\left(\frac{\sqrt{2}}{3}\right)^2\)
b)\(\left(-\sqrt{\frac{5}{4}}\right)^2-\sqrt{\frac{9}{4}}:\left(-4,5\right)-\sqrt{\frac{25}{16}}.\sqrt{\frac{64}{9}}\)
c)\(-2^4-\left(-2\right)^2:\left(-\sqrt{\frac{16}{121}}\right)-\left(-\sqrt{\frac{2}{3}}\right)^2:\left(-2\frac{2}{3}\right)\)
rút gon
a,\(\frac{2.5^{22}-9.5^{21}}{25^{10}}\)
b,\(\frac{5\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}\)
c,\(\frac{\left(\left(-2\right)^2\right)^3.\left(-4\right)^2}{\left(-2\right)^3.\left(-2\right)^2}\)
d,\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
e,\(2^3+3.\left(\frac{1}{8}\right)^0-\left(\frac{1}{2^2}\right).4+\left[\left(-2\right)^2:\frac{1}{2}\right].8\)
f,\(\frac{\left(\frac{2}{5}\right)^7.5^5+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2+512}\)
Cũng khuya rồi , mình làm câu 1 thôi nhé !
\(\frac{2.5^{22}-9.5^{21}}{25^{10}}=\frac{2.5^{22}-9.5^{21}}{\left(5^2\right)^{10}}\)
\(\frac{5^{21}.\left(2.5-9\right)}{5^{20}}=5.\left(10-9\right)=5\)
\(A=\frac{1}{2}-\frac{3}{4}+\frac{5}{6}-\frac{7}{12}\)
\(B=3-\frac{2}{3}+\frac{3}{5}\left(-\frac{10}{9}-\frac{25}{3}\right)-\frac{5}{6}\)
\(\left(3-\frac{3}{4}+\frac{2}{3}\right)-\left(2+\frac{4}{3}-\frac{3}{2}\right)-\left(1-\frac{7}{3}-\frac{9}{2}\right)\)
\(D=\left[-\frac{54}{64}-\left(\frac{1}{9}:\frac{8}{27}\right):-\frac{1}{3}\right]:-\frac{81}{128}\)
\(-\frac{3}{5}+\frac{2}{61}-\frac{17}{51}\)
\(\left(\frac{3}{2}-\frac{5}{11}-\frac{3}{13}\right)+\left(\frac{3}{4}+\frac{5}{22}+\frac{3}{26}\right)\)
\(\frac{1}{4}-3\cdot\left(\frac{1}{12}+\frac{3}{8}\right)\)
\(\left(-\frac{2}{3}+\frac{3}{5}\right):\frac{1}{50}-30\)
\(\left(-\frac{4}{5}+\frac{5}{7}\right):\frac{3}{17}+\left(-\frac{1}{5}+\frac{2}{7}\right):\frac{3}{17}\)
\(\frac{1}{3}-\frac{1}{7}+\frac{8}{9}+\frac{15}{12}-\frac{3}{5}-\frac{2}{3}\)
► Các cậu giúp mình nha. Mình sẽ tick cho ai có đáp án nhanh nhất và đúng nhất nhé. Mình cảm ơn tất cả các cậu trước ạ. Kamsa~
Những câu từ D trở đi là các câu riêng biệt ak bạn
\(A = {1\over2}-{3\over4}+{5\over6}-{7\over12}={6\over12}-{9\over12}+{10\over12}-{7\over12}\)\(={0\over12}=0\)
\(B=3-{2\over3}+{3\over5}(-{10\over9}-{25\over3})-{5\over6}\)\(={7\over3}+{3\over5}(-{10\over9}-{75\over9})-{5\over6}\)\(={14\over6}-{5\over6}+{3\over5}({-85\over9})\)\(={3\over2}-{17\over3}={9\over6}-{34\over6}={-25\over6}\)
Tính
a) \(-1\frac{5}{7}x15+\frac{2}{7}x\left(-15\right)+\left(-105\right)x\left(\frac{2}{3}-\frac{4}{5}+\frac{1}{7}\right)\)
b) \(\frac{3^6x45^4-15^{13}x5^{-9}}{27^4x25^3+45^6}\)
c) \(\frac{\left(\frac{2}{5}\right)^7x5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7x5^2+512}\)
Bài 1: Thực hiện phép tính
a) 3 2 . \(\frac{1}{243}\). 81 2 . 3 -3
b) \(\frac{\left(-3\right)^{10}.15^5}{25^3.\left(-9\right)^7}\)
c) 2 3 + 3.\(\left(\frac{1}{3}\right)^0\)-2 -2 .4+\(\left[\left(-2\right)^2:\frac{1}{2}\right]\).8
d)\(\left(\frac{-3}{4}\right)^4:\left(\frac{-9}{8}\right)^4\)
e) \(\left(\frac{-31}{8}\right)^3.\left(\frac{-32}{31}\right)^4\)
f) \(\left(-\frac{3}{4}\right)^5.\left(\frac{16}{9}\right)^5\)
giải giúp mình nha !!!
Gửi tạm trước 2 câu !
\(a,\text{ }3^2\cdot\frac{1}{243}\cdot81^2\cdot3^{-3}=3^2\cdot\frac{1}{3^5}\cdot\left(3^4\right)^2\cdot\frac{1}{3^3}=3^2\cdot\frac{1}{3^5}\cdot3^8\cdot\frac{1}{3^3}=3^2=9\)\(b,\text{ }\frac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}=\frac{3^{10}\cdot\left(3\cdot5\right)^5}{\left(5^2\right)^3\cdot\left(-3\cdot3\right)^7}=\frac{3^{10}\cdot3^5\cdot5^5}{5^6\cdot3^7\cdot\left(-3\right)^7}=\frac{3^{15}\cdot5^5}{5^6\cdot3^7\cdot\left(-3\right)^7}=\frac{3}{-5}\)
Trả lời :
\(a,\text{ }3^2\cdot\frac{1}{243}\cdot81^2\cdot3^{-3}=3^2\cdot\frac{1}{3^5}\cdot\left(3^4\right)^2\cdot\frac{1}{3^3}=3^2\cdot\frac{1}{3^5}\cdot3^8\cdot\frac{1}{3^3}=3^2=9\)\(b,\text{ }\frac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}=\frac{3^{10}\cdot\left(3\cdot5\right)^5}{\left(5^2\right)^3\cdot\left(-3\cdot3\right)^7}=\frac{3^{10}\cdot3^5\cdot5^5}{5^6\cdot3^7\cdot\left(-3\right)^7}=\frac{3^{15}\cdot5^5}{5^6\cdot3^7\cdot\left(-3\right)^7}=\frac{3}{-5}\)
1,Tính : ( Hãy tính nhanh nếu có thể )
a,\(\frac{3^6.45^4-15^{13}.\left(\frac{1}{5}\right)^9}{27^4.25^3+45^6}\)
b,\(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2+512}\)
15. Tính:
a) \(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
b) \(\frac{\left(\frac{2}{7}\right)^7.5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2+512}\)
mình cần lắm ạ, tối nay phải nộp rồi cám ơn các bn trc :''(
15: Tính
a) Ta có: \(\frac{3^6\cdot45^4-15^{13}\cdot5^{-9}}{27^4\cdot25^3+45^6}\)
\(=\frac{3^6\cdot3^4\cdot15^4-15^{13}\cdot\frac{1}{5^9}}{9^4\cdot3^4\cdot5^6+9^6\cdot5^6}\)
\(=\frac{3^6\cdot45^4-\frac{5^{13}\cdot3^{13}}{5^9}}{9^4\cdot5^6\left(3^4+9^2\right)}\)
\(=\frac{45^4\cdot3^6-5^4\cdot3^{13}}{45^4\cdot5^2\cdot2\cdot9^2}\)
\(=\frac{5^4\cdot3^6\left(9^4-3^7\right)}{5^2\cdot3^4\cdot45^4\cdot2}\)
\(=\frac{5^2\cdot3^2\cdot\left(3^8-3^7\right)}{45^4\cdot2}\)
\(=\frac{5^2\cdot3^9\cdot\left(3-1\right)}{5^4\cdot3^8\cdot2}\)
\(=\frac{1}{5^2}\cdot3\)
\(=\frac{3}{25}\)
Bài 1: Tính a) \(\left(\frac{11}{12}:\frac{44}{16}\right)\cdot\left(\frac{-1}{3}+\frac{1}{2}\right)\) b) \(\frac{\left(-5^2\right)\cdot\left(-5\right)^3\cdot16}{5^4\cdot\left(-2\right)^4}\) c) \(7,5:\left(\frac{-5}{3}\right)+2\frac{1}{2}:\left(\frac{-5}{3}\right)\)d) \(\left(\frac{-1}{2}+\frac{1}{3}\right)\cdot\frac{4}{5}+\left(\frac{2}{3}+\frac{1}{2}\right):\frac{4}{5}\)
a) \(\left(\frac{11}{12}:\frac{44}{16}\right).\left(\frac{-1}{3}+\frac{1}{2}\right)\) \(=\left(\frac{11}{12}.\frac{16}{44}\right).\left(\frac{-2}{6}+\frac{3}{6}\right)\) \(=\frac{1}{3}.\frac{1}{6}\) \(=\frac{1}{18}\)
b) \(\frac{\left(-5\right)^2.\left(-5\right)^3.16}{5^4.\left(-2\right)^4}\) \(=\frac{\left(-5\right)^5.2^4}{5^4.\left(-2\right)^4}\) \(=5\) (Có sửa đề lại, nếu có sai thì ib mình sửa lại nhé!)
c) \(7,5:\left(\frac{-5}{3}\right)+2\frac{1}{2}:\left(\frac{-5}{3}\right)\) \(=\frac{15}{2}.\left(\frac{-3}{5}\right)+\frac{5}{2}.\left(\frac{-3}{5}\right)\) \(=\frac{-3}{5}.\left(\frac{15}{2}+\frac{5}{2}\right)\)
\(=\frac{-3}{5}.10\) \(=-6\)
d) \(\left(\frac{-1}{2}+\frac{1}{3}\right).\frac{4}{5}+\left(\frac{2}{3}+\frac{1}{2}\right):\frac{5}{4}\) \(=\left(\frac{-1}{2}+\frac{1}{3}\right).\frac{4}{5}+\left(\frac{2}{3}+\frac{1}{2}\right).\frac{4}{5}\)
\(=\frac{4}{5}.\left(\frac{-1}{2}+\frac{1}{3}+\frac{2}{3}+\frac{1}{2}\right)\) \(=\frac{4}{5}.\left(\frac{0}{2}+1\right)\) \(=\frac{4}{5}.1=\frac{4}{5}\)
a) (1112:4416).(−13+12)(1112:4416).(−13+12) =(1112.1644).(−26+36)=(1112.1644).(−26+36) =13.16=13.16 =118=118
b) (−5)2.(−5)3.1654.(−2)4(−5)2.(−5)3.1654.(−2)4 =(−5)5.2454.(−2)4=(−5)5.2454.(−2)4 =5=
c) 7,5:(−53)+212:(−53)7,5:(−53)+212:(−53) =152.(−35)+52.(−35)=152.(−35)+52.(−35) =−35.(152+52)=−35.(152+52)
=−35.10=−35.10 =−6=−6
d) (−12+13).45+(23+12):54(−12+13).45+(23+12):54 =(−12+13).45+(23+12).45=(−12+13).45+(23+12).45
=45.(−12+13+23+12)=45.(−12+13+23+12) =45.(02+1)=45.(02+1) =45.1=45