a) Ta có:

12⁸ = (12²)⁴ = 144⁴

8¹² = (8³)⁴ = 512⁴

Vì 144⁴ < 512⁴

=> 12⁸ < 8¹²

b) (-5)³⁹ = -5³⁹ =-(5³)¹³ = -125¹³

(-2)⁹¹ = -2⁹¹ = -(2⁷)¹³ = -128¹³

Vì -125¹³ > -128¹³

=> (-5)³⁹ > (-2)⁹¹

a/ Ta có :

\(12^8=\left(12^2\right)^4=24^4\)

\(8^{12}=\left(8^3\right)^4=512^4\)

Vì \(24^4< 512^4\Leftrightarrow12^8< 8^{12}\)

b/ Ta có :

\(\left(-5\right)^{39}=\left[\left(-5\right)^3\right]^{13}=\left(-125\right)^{13}\)

\(\left(-2\right)^{91}=\left[\left(-2\right)^7\right]^{13}=\left(-128\right)^{13}\)

Vì \(\left(-125\right)^{13}>\left(-128\right)^{13}\Leftrightarrow\left(-5\right)^{39}>\left(-2\right)^{91}\)

\(1,\\ a,2< 3\Rightarrow2^{30}< 3^{30}\Rightarrow-2^{30}>-3^{30}\\ b,6^{10}=6^{2\cdot5}=\left(6^2\right)^5=36^5>35^5\left(36>35\right)\)

\(2,\\ a,\dfrac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}=\dfrac{3^{10}\cdot5^5\cdot3^5}{5^6\cdot3^{14}}=\dfrac{3}{5}\\ b,\left(8x-1\right)^{2x+1}=5^{2x+1}\\ \Leftrightarrow8x-1=5\\ \Leftrightarrow x=\dfrac{3}{4}\)

Bài 2: 

a: Ta có: \(\dfrac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}\)

\(=\dfrac{-3^{10}\cdot3^5\cdot5^5}{5^6\cdot3^{14}}\)

\(=-\dfrac{3}{5}\)

b: Ta có: \(\left(8x-1\right)^{2x+1}=5^{2x+1}\)

\(\Leftrightarrow8x-1=5\)

\(\Leftrightarrow8x=6\)

hay \(x=\dfrac{3}{4}\)

Bài 1: 

a: \(-2^{30}=-8^{10}\)

\(-3^{30}=-27^{10}\)

mà 8<27

nên \(-2^{30}>-3^{30}\)

b: \(35^5=35^5\)

\(6^{10}=36^5\)

mà 35<36

nên \(35^5< 6^{10}\)

Bài1:

\(a,\left(-8\right)^9\) và \(\left(-32\right)^5\)

Ta có:

\(\left(-8\right)^9=-2^{27}\)

\(\left(-32\right)^5=\left(-8.4\right)^5=-2^{27}.2^{10}\)

Vì \(-2^{27}.10< -2^{27}\) nên \(\left(-8\right)^9>\left(-32\right)^5\)

Các câu sau tương tự

Bài2:

\(a,2\left|x-1\right|-3x=7\)

+)Xét \(x\ge1\Rightarrow\left|x-1\right|=x-1\)

Do đó:

\(2\left(x-1\right)-3x=7\\ \Leftrightarrow2x-2-3x=7\\ \Leftrightarrow-x=9\\ \Leftrightarrow x=-9\left(loại\right)\)

+)Xét \(x< 1\Rightarrow\left|x-1\right|=1-x\)

Do đó:

\(2\left(1-x\right)-3x=7\\ \Leftrightarrow2-2x-3x=7\\ \Leftrightarrow-5x=5\\ x=-1\left(chon\right)\)

Vậy x=-1

Câu b tương tự

Bài 1:

\(a,\left(-8\right)^9\) và \(\left(-32\right)^5\)

\(\left(-8\right)^9=\left[\left(-2\right)^3\right]^9=\left(-2\right)^{27}\)

\(\left(-32\right)^5=\left[\left(-2\right)^5\right]^5=\left(-2\right)^{25}\)

\(\left(-2\right)^{27}< \left(-2\right)^{25}\)

\(\Rightarrow\left(-8\right)^9< \left(-32\right)^5\)

\(b,2^{21}\) và \(3^{14}\)

\(2^{21}=\left(2^3\right)^7\)

\(3^{14}=\left(3^2\right)^7\)

\(2^3< 3^2\)\(\Rightarrow2^{21}< 3^{14}\)

\(c,12^8\) và \(8^{12}\)

\(12^8=\left(12^2\right)^4=144^4\)

\(8^{12}=\left(8^3\right)^4=512^4\)

\(144^4< 512^4\)\(\Rightarrow12^8< 8^{12}\)

\(d,\left(-5\right)^{39}\) và \(\left(-2\right)^{91}\)

\(\left(-5\right)^{39}=\left[\left(-5\right)^3\right]^{13}\)

\(\left(-2\right)^{91}=\left[\left(-2\right)^7\right]^{13}\)

\(\left(-5\right)^3>\left(-2\right)^7\)\(\Rightarrow\left(-5\right)^{39}>\left(-2\right)^{91}\)

Bài 2:

\(a,2.\left|x-1\right|-3x=7\)

\(\left|x-1\right|=\dfrac{7+3x}{2}\)

Ta có 2 trường hợp:

Th1:\(x-1=\dfrac{7-3x}{2}\)

\(\dfrac{2x-2}{2}=\dfrac{7+3x}{2}\)

\(\Rightarrow2x-2=7+3x\)

\(2x-3x=7+2\)

\(-x=9\Rightarrow x=-9\)

Th2:\(x+1=-\dfrac{7+3x}{2}\)

\(\dfrac{2x-2}{2}=\dfrac{-7-3x}{2}\)

\(\Rightarrow2x-2=-7-3x\)

\(2x+3x=-7+2\)

\(5x=-5\Rightarrow x=-1\)

Vậy \(x\in\left\{-9;-1\right\}\)

\(b,\left|5x-3\right|=\left|7-x\right|\)

Ta có: Th1: \(\left|7-x\right|=7-x\) khi \(7-x\ge0\)\(\Rightarrow x\le7\)

\(5x-3=7-x\)

\(5x+x=7+3\)

\(6x=10\Rightarrow x=\dfrac{10}{6}=\dfrac{5}{3}\)( thoả mãn )

vì x thoả mãn \(x\le7\)\(\Rightarrow\) th1 thoả mãn x

Ta có: Th2: \(\left|7-x\right|=-\left(7-x\right)\) khi \(7-x< 0\Rightarrow x>7\)

\(5x-3=-\left(7-x\right)\)

\(5x-3=-7+x\)

\(5x-x=-7+3\)

\(4x=-4\Rightarrow x=-1\) ( loại )

Vì x thoả mãn \(x>7\) mà \(x=-1\Rightarrow\)th2 loại

bài 1

a) (-8)⁹ và (-32)⁵

=[(-2)³]⁹ và [(-2)⁵]⁵

=(-2)²⁷ và (-2)²⁵

vì 27 >25

=>(-2)²⁷<(-2)²⁵ hay(-8)⁹ <(-32)⁵

ngu như con lợn

chịu thôi

B=64,8

a,

A = 5.(2² . 3² )⁹. (2²)⁶ - 2. (2².3)¹⁴.3⁴ / 5.2²⁸.3¹⁸ - 7.2²⁹.3¹⁸

A = 5.2¹⁸.3¹⁸.2¹² - 2. 2^28. 3¹⁴. 3⁴ / 5. 2²⁸. 3¹⁸ - 7. 2²⁹. 3¹⁸

A = 5.2³⁰.3¹⁸ - 2²⁹. 3¹⁸ /  5.2 ²⁸.3¹⁸ - 7.2²⁹. 3¹⁸

A = 2²⁹. 3¹⁸(5.2-1) / 2²⁸. 3¹⁸ (5 -7.2)

A = 2.9 / -9 = -2

Vậy A = -2

b,

B =81.( 12 - 12/7- 12/289 - 12/85 /  4 - 4/7 - 4/289 - 4/85 :

5 + 5/13 + 5/169 + 5/91 /  6 + 6/13 + 6/169 + 5/91 ) x 158158158

B = 81.[ 12.( 1 - 1/7 - 1/289 - 1/85) / 4.( 1 - 1/7 - 1/289 - 1/85 :

5.(1 + 1/13 + 1/169 + 1/91) / 6.(1+ 1/13 +1/169 + 1/91)] . 2/9

B = 81.[ 3 : 5/6 ] .2/9

B = 81.18/5 . 2/9

B = 1458/5 . 2/9

B = 324/5.

Vậy B = 324/5

CHÚC HỌC TỐT

\(a)\) \(A=\frac{5\left(2^2.3^2\right)^9.\left(2^2\right)^6-2\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)

\(A=\frac{2^{30}.3^{18}.5-2^{29}.3^{18}}{2^{28}.3^{18}.5-2^{29}.3^{18}.7}\)

\(A=\frac{2^{29}.3^{18}\left(2.5-1\right)}{2^{28}.3^{18}\left(5-2.7\right)}\)

\(A=\frac{2\left(10-1\right)}{5-14}\)

\(A=\frac{2.9}{-9}\)

\(A=-2\)

Vậy \(A=-2\)

\(b)\) \(B=81.\left[\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right].\frac{158158158}{711711711}\)

\(B=81.\left[\frac{12\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}{4\left(1-\frac{1}{7}-\frac{1}{289}-\frac{1}{85}\right)}:\frac{5\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}{6\left(1+\frac{1}{13}+\frac{1}{169}+\frac{1}{91}\right)}\right].\frac{158158158}{711711711}\)

\(B=81.\left[\frac{12}{4}:\frac{5}{6}\right].\frac{2}{9}\)

\(B=81.\frac{18}{5}.\frac{2}{9}\)

\(B=\frac{324}{5}\)

Vậy \(B=\frac{324}{5}\)

Chúc bạn học tốt ~ ( mỏi tay qué >_< ) 

Đưa về cùng số mũ hoặc cơ số nhé !

a, Đưa về cùng cơ số4

b, Đưa về cùng số mũ 13 

chúc bạn học tốt ^-^

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