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17 tháng 12 2023

a: \(\left(\dfrac{3}{4}-81\right)\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

\(=\left(\dfrac{3^6}{9}-81\right)\left(\dfrac{3}{4}-81\right)\cdot\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

\(=\left(81-81\right)\left(\dfrac{3}{4}-81\right)\cdot\left(\dfrac{3^2}{5}-81\right)\cdot...\cdot\left(\dfrac{3^{2000}}{2003}-81\right)\)

=0

b: \(\dfrac{69}{157}-\left(2+\left(3+4+5^{-1}\right)^{-1}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+\left(3+4+\dfrac{1}{5}\right)^{-1}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+1:\dfrac{36}{5}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(2+\dfrac{5}{36}\right)^{-1}\)

\(=\dfrac{69}{157}-\left(\dfrac{77}{36}\right)^{-1}\)

\(=\dfrac{69}{157}-\dfrac{36}{77}=\dfrac{-339}{12089}\)

12 tháng 7 2018

a)\(\left(\frac{3}{5}\right)^5\times x=\left(\frac{3}{7}\right)^7\)

\(\Leftrightarrow\frac{3^5}{5^5}\times x=\frac{3^7}{7^7}\)

\(\Leftrightarrow x=\frac{3^7}{7^7}:\frac{3^5}{5^5}\)

\(\Leftrightarrow x=\frac{3^7\times5^5}{7^7\times3^5}\)

\(\Leftrightarrow x=\frac{3^2\times5^5}{7^7}\)

b)\(\left(\frac{-1}{3}\right)^3\times x=\frac{1}{81}\)

\(\Leftrightarrow\frac{\left(-1\right)^3}{3^3}\times x=\frac{1}{3^4}\)

\(\Leftrightarrow x=\frac{1}{3^4}:\frac{-1}{3^3}\)

\(\Leftrightarrow x=\frac{1\times3^3}{3^4\times\left(-1\right)}\)

\(\Leftrightarrow x=\frac{1}{-3}\)

c)\(\Leftrightarrow\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{3}\right)^3\)

\(\Leftrightarrow x-\frac{1}{2}=\frac{1}{3}\)

\(\Leftrightarrow x=\frac{1}{3}+\frac{1}{2}\)

\(\Leftrightarrow x=\frac{5}{6}\)

d)\(\Leftrightarrow\left(x+\frac{1}{2}\right)^4=\left(\frac{2}{3}\right)^4\)

\(\Leftrightarrow x+\frac{1}{2}=\frac{2}{3}\)

\(\Leftrightarrow x=\frac{2}{3}-\frac{1}{2}\)

\(\Leftrightarrow x=\frac{1}{6}\)

10 tháng 12 2022

Câu 2

(a+3)(b-4)-(a-3)(b+4)=0

=>ab-4a+3b-12-ab-4a+3b+12=0

=>-8a=-6b

=>a/b=3/4

=>a/3=b/4

12 tháng 11 2016

tu hoc moi gioi

21 tháng 6

nói vậy thì những bài khó tự đi mà làm ngồi đó mà sĩ

 

b: \(9x^2+54+81=\left(3x+9\right)^2\)

c: \(=\left(y-\dfrac{1}{2}\right)^2\)

d: \(=\left(4x^3-3\right)^2\)

6 tháng 8 2023

\(\sqrt{\dfrac{4}{81}}\div\sqrt{\dfrac{25}{81}}-1\dfrac{3}{5}=\dfrac{2}{9}\div\dfrac{5}{9}-\dfrac{8}{5}\)

                                 \(=\dfrac{2}{5}-\dfrac{8}{5}=\dfrac{-6}{5}\)

16 tháng 12 2018

a,

\(\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)

\(\dfrac{1}{4}:x=\dfrac{2}{5}-\dfrac{3}{4}\\ \)

\(\dfrac{1}{4}:x=\dfrac{8-15}{20}\)

\(\dfrac{1}{4}:x=\dfrac{-7}{20}\)

x = \(\dfrac{1}{4}:\dfrac{-7}{20}\)

\(x=\dfrac{-5}{7}\)

b,

( 3x + 1)^3 = 64

(3x + 1)^3 = 4^3

(3x + 1) = 4

3x = 4 - 1

3x = 3

x = 3 : 3

x = 1

c,

( 2x - 3)^4 = 81

( 2x - 3) ^4 = 3^4

(2x - 3) = 3

2x = 3 + 3

2x = 6

x = 6: 2

x = 3