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títtt
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a: \(A=\dfrac{9^4}{3^2}=\dfrac{\left(3^2\right)^4}{3^2}=\dfrac{3^8}{3^2}=3^6\)=729

b: \(B=81\left(\dfrac{5}{3}\right)^4=81\cdot\dfrac{5^4}{3^4}=\dfrac{81}{3^4}\cdot5^4=5^4=625\)

c: \(C=\left(\dfrac{4}{7}\right)^{-4}\cdot\left(\dfrac{2}{7}\right)^3\)

\(=\left(\dfrac{7}{4}\right)^4\cdot\left(\dfrac{2}{7}\right)^3\)

\(=\dfrac{7^4}{4^4}\cdot\dfrac{2^3}{7^3}\)

\(=\dfrac{2^3}{4^4}\cdot7\)

\(=\dfrac{2^3}{2^8}\cdot7=\dfrac{7}{2^5}=\dfrac{7}{32}\)

d: \(D=7^{-6}\cdot\left(\dfrac{2}{3}\right)^0\left(\dfrac{7}{5}\right)^6\)

\(=7^{-6}\left(\dfrac{7}{5}\right)^6\)

\(=\dfrac{1}{7^6}\cdot\dfrac{7^6}{5^6}=\dfrac{1}{5^6}=\dfrac{1}{15625}\)

e: \(E=8^3:\left(\dfrac{2}{3}\right)^5\cdot\left(\dfrac{1}{3}\right)^2\)

\(=2^6:\dfrac{2^5}{3^5}\cdot\dfrac{1}{3^2}\)

\(=2^6\cdot\dfrac{3^5}{2^5}\cdot\dfrac{1}{3^2}\)

\(=\dfrac{2^6}{2^5}\cdot\dfrac{3^5}{3^2}=3^3\cdot2=54\)

f: \(F=\left(\dfrac{7}{9}\right)^{-2}\cdot\left(\dfrac{1}{\sqrt{3}}\right)^8\)

\(=\left(\dfrac{9}{7}\right)^2\cdot\left(\dfrac{1}{3}\right)^4\)

\(=\dfrac{9^2}{7^2}\cdot\dfrac{1}{3^4}=\dfrac{9^2}{3^4}\cdot\dfrac{1}{7^2}=\dfrac{81}{81}\cdot\dfrac{1}{49}=\dfrac{1}{49}\)

g: \(G=\left(-\dfrac{4}{5}\right)^{-2}\cdot\left(\dfrac{2}{5}\right)^2\cdot\left(\sqrt{2}\right)^3\)

\(=\left(-\dfrac{5}{4}\right)^2\cdot\left(\dfrac{2}{5}\right)^2\cdot2\sqrt{2}\)

\(=\dfrac{25}{16}\cdot\dfrac{4}{25}\cdot2\sqrt{2}=\dfrac{4}{16}\cdot2\sqrt{2}=\dfrac{8\sqrt{2}}{16}=\dfrac{\sqrt{2}}{2}\)

The Maker(TPCT)
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Nguyễn Việt Hoàng
11 tháng 2 2020 lúc 16:58

a) \(2\left(x-5\right)-3\left(x+7\right)=14\)

\(\Leftrightarrow2x-10-3x-21=14\)

\(\Leftrightarrow-x-31=14\)

\(\Leftrightarrow-x=45\Leftrightarrow x=-45\)

b) \(5\left(x-6\right)-2\left(x+3\right)=12\)

\(\Leftrightarrow5x-30-2x-6=12\)

\(\Leftrightarrow3x-36=12\)

\(\Leftrightarrow3x=48\Leftrightarrow x=16\)

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Nguyễn Việt Hoàng
11 tháng 2 2020 lúc 17:02

c) \(3\left(x-4\right)-\left(8-x\right)=12\)

\(\Leftrightarrow3x-12-8+x=12\)

\(\Leftrightarrow4x-20=12\)

\(\Leftrightarrow4x=32\Leftrightarrow x=8\)

d) \(-7\left(3x-5\right)+2\left(7x-14\right)=28\)

\(\Leftrightarrow-21x+35+14x-28=28\)

\(\Leftrightarrow-7x+35=0\Leftrightarrow x=5\)

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Nguyễn Việt Hoàng
11 tháng 2 2020 lúc 17:07

e)\(5\left(3-2x\right)+5\left(x-4\right)=6-4x\)

\(\Leftrightarrow15-10x+5x-20=6-4x\)

\(\Leftrightarrow-5-5x=6-4x\)

\(\Leftrightarrow-5x+4x=5+6\)

\(\Leftrightarrow-x=11\Leftrightarrow x=-11\)

f) \(-5\left(2-x\right)+4\left(x-3\right)=10x-15\)

\(\Leftrightarrow-10+5x+4x-12=10x-15\)

\(\Leftrightarrow-22+9x-10x+15=0\)

\(\Leftrightarrow-7-x=0\Leftrightarrow x=-7\)

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LÊ TRẦN BÁCH
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Nguyễn Đăng Nhân
20 tháng 9 2023 lúc 19:43

a) \(\left(x-1\right)^3=8=2^3\)

\(x-1=2\)

\(x=2+1=3\)

b) \(7^{2x-6}=49=7^2\)

\(2x-6=2\)

\(2x=6+2=8\)

\(x=8:2=4\)

c) \(\left(2x-14\right)^7=128=2^7\)

\(2x-14=2\)

\(2x=14+2=16\)

\(x=16:2=8\)

d) \(x^4\cdot x^5=5^3\cdot5^6=5^4\cdot5^5\)

\(x=5\)

e) \(3\cdot\left(x+2\right):7\cdot4=120\)

\(x+2=120:3\cdot7:4\)

\(x+2=70\)

\(x=70-2=68\)

Akai Haruma
20 tháng 9 2023 lúc 21:15

Lời giải:

a. $(x-1)^3=8=2^3$
$\Rightarrow x-1=2$

$\Rightarrow x=3$

b. $7^{2x-6}=49=7^2$
$\Rightarrow 2x-6=2$

$\Rightarrow 2x=8$

$\Rightarrow x=4$

c. $(2x-14)^7=128=2^7$

$\Rightarrow 2x-14=2$

$\Rightarrow 2x=16$

$\Rightarrow x=18$

d.

$x^4.x^5=5^3.5^6$

$x^9=5^9$

$\Rightarrow x=5$

e. 

$3(x+2):7=120:4=30$

$3(x+2)=30.7=210$

$x+2=210:3=70$

$x=70-2=68$

Nguyen Le Tuong Vy
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HT.Phong (9A5)
12 tháng 7 2023 lúc 18:07

a) \(A=\left(-0,75-\dfrac{1}{4}\right):\left(-5\right)+\dfrac{1}{48}-\left(-\dfrac{1}{6}\right):\left(-3\right)\)

\(A=\left(-0,75-0,25\right):\left(-5\right)+\dfrac{1}{48}-\left(-\dfrac{1}{6}\right)\cdot\dfrac{-1}{3}\)

\(A=\left(-1\right):\left(-5\right)+\dfrac{1}{48}-\dfrac{1}{18}\)

\(A=\dfrac{1}{5}+\dfrac{1}{48}-\dfrac{1}{18}\)

\(A=\dfrac{119}{720}\)

b) \(B=\left(\dfrac{6}{25}-1,24\right):\dfrac{3}{7}:\left[\left(3\dfrac{1}{2}-3\dfrac{2}{3}\right):\dfrac{1}{14}\right]\)

\(B=\left(0,24-1,24\right):\dfrac{3}{7}:\left[\left(\dfrac{7}{2}-\dfrac{11}{3}\right):\dfrac{1}{14}\right]\)

\(B=-1:\dfrac{3}{7}:\left(-\dfrac{1}{6}:\dfrac{1}{14}\right)\)

\(B=-\dfrac{7}{3}:-\dfrac{7}{3}\)

\(B=1\)

a, A = (-0,75 - \(\dfrac{1}{4}\)) : (-5) + \(\dfrac{1}{48}\) - (- \(\dfrac{1}{6}\)) : (-3)

   A  = -(0,75 + 0,25): (-5) + \(\dfrac{1}{48}\) - \(\dfrac{1}{18}\)

   A = -1 : (-5) + \(\dfrac{1}{48}\) - \(\dfrac{1}{18}\)

   A = \(\dfrac{1}{5}\) + \(\dfrac{1}{48}\) - \(\dfrac{1}{18}\)

  A = \(\dfrac{53}{240}\) - \(\dfrac{1}{18}\)

 A = \(\dfrac{119}{720}\)

b, B = (\(\dfrac{6}{25}\) - 1,24): \(\dfrac{3}{7}\): [(3\(\dfrac{1}{2}\) - 3\(\dfrac{2}{3}\)): \(\dfrac{1}{14}\)]

    B = (0,24 - 1,24): \(\dfrac{3}{7}\):[(\(\dfrac{7}{2}\)-\(\dfrac{11}{3}\)): \(\dfrac{1}{14}\)]

    B = -1: \(\dfrac{3}{7}\):[ (-\(\dfrac{1}{6}\) : \(\dfrac{1}{14}\))]

   B  = -1: \(\dfrac{3}{7}\): (- \(\dfrac{7}{3}\))

B = 1 \(\times\) \(\dfrac{7}{3}\) \(\times\) \(\dfrac{3}{7}\)

B = 1

Nguyễn Đức Trí
12 tháng 7 2023 lúc 18:13

\(A=\left(-0,75-\dfrac{1}{4}\right):\left(-5\right)+\dfrac{1}{48}-\left(-\dfrac{1}{6}\right):\left(-3\right)\)

\(A=\left(-\dfrac{2}{4}-\dfrac{1}{4}\right).\left(-\dfrac{1}{5}\right)+\dfrac{1}{48}-\left(-\dfrac{1}{6}\right).\left(-\dfrac{1}{3}\right)\)

\(A=-\dfrac{3}{4}.\left(-\dfrac{1}{5}\right)+\dfrac{1}{48}-\dfrac{1}{18}\)

\(A=\dfrac{3}{20}+\dfrac{1}{48}-\dfrac{1}{18}=\dfrac{108}{720}+\dfrac{15}{720}-\dfrac{40}{720}=\dfrac{83}{720}\)

Từ Bảo
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Nguyễn Ngọc Lộc
27 tháng 6 2021 lúc 21:24

a, Ta thấy : \(\left\{{}\begin{matrix}\left(2a+1\right)^2\ge0\\\left(b+3\right)^2\ge0\\\left(5c-6\right)^2\ge0\end{matrix}\right.\)\(\forall a,b,c\in R\)

\(\Rightarrow\left(2a+1\right)^2+\left(b+3\right)^2+\left(5c-6\right)^2\ge0\forall a,b,c\in R\)

\(\left(2a+1\right)^2+\left(b+3\right)^2+\left(5c-6\right)^2\le0\)

Nên trường hợp chỉ xảy ra là : \(\left(2a+1\right)^2+\left(b+3\right)^2+\left(5c-6\right)^2=0\)

- Dấu " = " xảy ra \(\left\{{}\begin{matrix}2a+1=0\\b+3=0\\5c-6=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=-\dfrac{1}{2}\\b=-3\\c=\dfrac{6}{5}\end{matrix}\right.\)

Vậy ...

b,c,d tương tự câu a nha chỉ cần thay số vào là ra ;-;

pham thi hoa
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Trần Nguyễn Phương Thảo
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Võ Ngọc Phương
11 tháng 7 2023 lúc 18:30

Tính hợp lí: 

a) \(\left(-0,4\right)+\dfrac{3}{8}+\left(-0,6\right)\)

\(=\left[\left(-0,4\right)+\left(-0,6\right)\right]+\dfrac{3}{8}\)

\(=-1+\dfrac{3}{8}\)

\(=\dfrac{\left(-8\right)+3}{8}\)

\(=\dfrac{-5}{8}\)

b) \(\dfrac{4}{5}-1,8+0,375+\dfrac{5}{8}\)

\(=\dfrac{4}{5}-\dfrac{9}{5}+\dfrac{3}{8}+\dfrac{5}{8}\)

\(=-1+1\)

\(=0\\\)

c) \(\dfrac{7}{3}.\left(-2,5\right).\dfrac{6}{7}\)

\(=\dfrac{7}{3}.\dfrac{-5}{2}.\dfrac{6}{7}\)

\(=\dfrac{7}{3}.\dfrac{6}{7}.\dfrac{-5}{2}\)

\(=2.\dfrac{-5}{2}\)

\(=-5\)

d) \(\dfrac{7}{12}.\left(-2,34\right)-\dfrac{7}{12}.\left(-0,34\right)\)

\(=\dfrac{7}{12}.\left[\left(-2,34\right)+0,34\right]\)

\(=\dfrac{7}{12}.\left(-2\right)\)

\(=\dfrac{-7}{6}\)

e) \(\dfrac{-8}{3}.\dfrac{2}{11}-\dfrac{8}{3}:\dfrac{11}{9}\)

\(=\dfrac{8}{3}.\dfrac{-2}{11}-\dfrac{8}{3}.\dfrac{9}{11}\)

\(=\dfrac{8}{3}.\left(\dfrac{-2}{11}-\dfrac{9}{11}\right)\)

\(=\dfrac{8}{3}.-1\)

\(=\dfrac{-8}{3}\)

Chúc bạn học tốt

Trần Nguyễn Phương Thảo
11 tháng 7 2023 lúc 18:33

Cảm ơn nha.

Nguyễn Đức Trí
11 tháng 7 2023 lúc 18:38

a)\(\left(-0,4\right)+\dfrac{3}{8}+\left(-0,6\right)=\left(-\dfrac{4}{10}\right)+\dfrac{3}{8}+\left(-\dfrac{6}{10}\right)=-\dfrac{2}{5}+\dfrac{3}{8}-\dfrac{3}{5}=-\dfrac{2}{5}-\dfrac{3}{5}+\dfrac{3}{8}=-1+\dfrac{3}{8}=-\dfrac{5}{8}\)

b) \(\dfrac{4}{5}-1,8+0,375+\dfrac{5}{8}=\dfrac{4}{5}+\dfrac{5}{8}-1,425=\dfrac{57}{40}-\dfrac{1425}{1000}=\dfrac{57}{40}-\dfrac{57}{40}=0\)

c) \(\dfrac{7}{3}.\left(-2,5\right).\dfrac{6}{7}=\dfrac{7}{3}.\dfrac{6}{7}.\left(-\dfrac{25}{10}\right)=-5\)

d) \(\dfrac{7}{12}.\left(-2,34\right)-\dfrac{7}{12}.\left(-0,34\right)=\dfrac{7}{12}.\left(-2,34-0,34\right)=\dfrac{7}{12}.\left(-2,68\right)=\dfrac{7}{12}.\left(-\dfrac{268}{100}\right)=-\dfrac{7}{12}.\dfrac{4}{25}=-\dfrac{7}{75}\)

e) \(\dfrac{-8}{3}.\dfrac{2}{11}-\dfrac{8}{3}:\dfrac{11}{9}=-\dfrac{8}{3}.\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=-\dfrac{8}{3}.1=-\dfrac{8}{3}\)

Shine Anna
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Khánh Linh
1 tháng 8 2017 lúc 9:56

1. A = (-2)(-3) - 5.|-5| + 125.\(\left(-\dfrac{1}{5}\right)^2\)
= 6 - 25 + 125.\(\dfrac{1}{25}\)
= -19 + 5
= -14
@Shine Anna

Quang Duy
1 tháng 8 2017 lúc 9:53

Đăng ít thôi

Khánh Linh
1 tháng 8 2017 lúc 9:58

1. B = (-3).|-7| - (-4).|5| + \(\dfrac{1}{3}.\left|-9\right|\)
= -21 + 20 + 3
= 2
@Shine Anna

Nguyệt Tích Lương
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Nguyễn Hoàng Minh
7 tháng 10 2021 lúc 17:01

\(a,=5^3:5^2=5\\ b,=\left(\dfrac{3}{4}\right)^{5-3}=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}\\ c,=1728-512=1216\\ d,=x^{10}:x^8=x^2\\ e,=\left(-x\right)^{5-3}=\left(-x\right)^2=x^2\\ f,=\left(-y\right)^{5-4}=-y\)