Câu 3 :

A = 7776 . 8 - 2.243. 64

A = 62208 - 31104

A = 31104

Câu 1 :

a) \(12^5=3^5.4^5\)

b) \(20^6=4^6.5^6\)

c) \(54^3=6^3.9^3\)

Câu 2 :

a) \(3.5^{55}=3.\left(5^5\right)^{11}\)

b) \(4.3^{816}=4.\left(3^{17}\right)^{48}\)

c) \(9.8.7^{6412}=9.8.\left(7^{28}\right)^{229}\)

1)Đưa về lũy thừa cùng cơ số 2

8²=  \(\left(2^3\right)^2=2^6\)        32³= \(\left(2^5\right)^3=2^{15}\)          64⁴= \(\left(2^6\right)^4=2^{24}\)       4³= \(\left(2^2\right)^{^3}=2^6\)

2)Đưa về lũy thừa cùng cơ số 3

9³= \(\left(3^2\right)^3=3^6\)       27⁴=  \(\left(3^3\right)^4=3^{12}\)      9⁵= \(\left(3^2\right)^5=3^{10}\)      81⁶=   \(\left(3^4\right)^6=3^{24}\)

3)Đưa về lũy thừa cùng cơ số 2

 8³:4²= \(\left(2^3\right)^3:\left(2^2\right)^2=2^9:2^4=2^5\)    16²:32= \(\left(2^4\right)^2:2^5=2^8:2^5=2^3\)    

\(64^4:4^3=\left(2^6\right)^4:\left(2^2\right)^3=2^{24}:2^6=2^{18}\)    32³:8²= \(\left(2^5\right)^3:\left(2^3\right)^2=2^{15}:2^6=2^9\)

Bạn giải nốt hộ mình câu 4,,5,6 mình cảm ơn nhìu

4)Đưa về lũy thừa cùng cơ số 3

27⁴:9³=\(\left(3^3\right)^4:\left(3^2\right)^3=3^{12}:3^6=3^6\)    81^6:9⁵=  \(\left(3^4\right)^6:\left(3^2\right)^5=3^{24}:3^{10}=3^{14}\)   

9⁶ .27⁴:81⁵=\(\left(3^2\right)^6.\left(3^3\right)^4:\left(3^4\right)^5=3^{12}.3^{12}:3^{20}=3^4\)

5)Đưa về lũy thừa cùng cơ số 5

25⁷=  \(\left(5^2\right)^7=5^{14}\)    125³=  \(\left(5^3\right)^3=5^9\)   25⁷:5⁶=  \(\left(5^2\right)^7:5^6=5^{14}:5^6=5^8\)

125⁶:25⁷= \(\left(5^3\right)^6:\left(5^2\right)^7=5^{18}:5^{14}=5^4\)

6)Đưa về lũy thừa cùng cơ số 4

16²= \(\left(4^2\right)^2=4^4\)     64³=\(\left(4^3\right)^3=4^9\)      (128:2)³=\(64^3=\left(4^3\right)^3=4^9\)     2².2²=\(4.4=4^2\)

\(125=5^3\) 

\(25^2=\left(5^2\right)^2=5^{2.2}=5^4\)

\(\left(5^3\right)^2=5^{3.2}=5^6\)

\(125^5=\left(5^3\right)^5=5^{3.5}=5^{15}\)

\(625^4=\left(5^4\right)^4=5^{4.4}=5^{16}\)

\(125.5^2=5^3.5^2=5^{3+2}=5^5\)

125 = 5³

25²  = (5²)² = 5⁴

(5³)² = 5⁶ 

125⁵ = ( 5³)⁵ = 5¹⁵

625⁴ = (5⁴)⁴ = 5¹⁶

125 . 5² = 5³ . 5² = 5⁵

a) = 2^12 . 2^2 . 2^40

 = 2^12+2+40

= 2^54

b)= 3^5 . 3^3 . 3^8

 = 3⁵⁺³⁺⁸

  =  3^16

c)= 5^4 . 5^2 . 5^3

= 5^{4 + 2 +3} 

= 5^9

a) 8⁴. 2².16¹⁰ = (2³)⁴.2².(2⁴ )¹⁰= 2¹² .2².2⁴⁰=2⁵⁴

b)  3⁵.27.81² =  3⁵.3³.( 3⁴) ² = 3⁵ . 3³.3⁸  = 3¹⁶

c)  25².5².125 =(5²)² .5².5³= 5⁴.5².5³= 5⁹

Trung Thu vui vẻ nha thuy hang

a, 

Ta có :  \(125^5=\left(5^3\right)^5=5^{15}\)

            \(25^7=\left(5^2\right)^7=5^{14}\)
do \(5^{15}>5^{14}\Rightarrow125^5>25^7\)

bài 1 : b

 1, cái này cùng mũ rồi mà bạn ?

 2, ta có : 

\(3^{54}=\left(3^6\right)^9=729^9\)

\(2^{81}=\left(2^9\right)^9=512^9\)

do \(729^9>512^9\Rightarrow3^{54}>2^{81}\)

a)\(4^3.2^4\div\left(4^2.\frac{1}{32}\right)\)

\(=\left(2^2\right)^3.2^4\div\left(2^2\right)^2\div32\).

\(=2^{\left(2.3\right)}.2^4\div2^{\left(2.2\right)}\div2^5\)

\(=2^6.2^4\div2^4\div2^5\)

\(=2^{6+4-4-5}=2^1\)

b)\(\left(\frac{1}{5}\right)^5=\frac{1}{5^5}=\left|5^5\right|=5^{-5}\)

\(\frac{1}{125}=\frac{1}{5^3}=\left|5^3\right|=5^{-3}\)

c)\(\frac{4}{25}=\frac{2^2}{5^2}=\left(\frac{2}{5}\right)^2=0,4^2\)

\(\frac{-8}{125}=\frac{-2^3}{5^3}=\left(\frac{-2}{5}\right)^2=-0,4^3=0,4^{-3}\)

\(\frac{16}{625}=\frac{2^4}{5^4}=\left(\frac{2}{5}\right)^4=0,4^4\)

1=1^2 ;125=5^3 ;-125=-5^3; 27=27^1; -27= -27^1

2: 5^2 25^1 

125:5

=(5.5.5):5

=5³:5

=5^3-1

=5²

125 : 5

= ( 5 . 5 . 5 ) : 5

=          5³    : 5

=             5²