a) \(625^4:25^7\)

\(=\left[25^2\right]^4:25^7\)

\(=25^8:25^7\)

\(=25\)

b)\(\left(100^5-89^5\right).\left(6^8-8^6\right).\left(8^2-4^3\right)\)

\(=\left(100^5-89^5\right).\left(6^8-8^6\right).\left[\left(2^3\right)^2-\left(2^2\right)^3\right]\)

\(=\left(100^5-89^5\right).\left(6^8-8^6\right).\left[2^6-2^6\right]\)

\(=\left(100^5-89^5\right).\left(6^8-8^6\right).0\)

\(=0\)

1. a) 3^2 .2^2 .2^4 = 3^2. 2^(2+4)=3^2. 2^6

     b) 10^2. 10^3.10^5= 10^(2+3+5)= 10^10

      c) x.x^5=x^(1+5)=x^6

      d) a^3 .a^2 ,a^5= a^(3+2+5)= a^10

2. a) 2^3 và 3^2 . Ta có: 2^3 = 8, 3^2=9 => 2^3 < 3^2

    b) 2^4 và 4^2. Ta có: 2^4= 16, 4^2=16 => 2^4 = 4^2

    c) 2^5 và 5^2. Ta có: 2^5= 32, 5^2=25 => 2^5 > 5^2

    d) 2^100 và 100.  => 2^100 > 100

3. a) 3^8:3^4= 3^(8-4)=3^4

    b) 10^8:10^2=10^(8-6)=10^2

    c) a^6: a (a#0) = a^(6-1)=a^5

dài quá bạn ơi mik làm được nhưng mà mik làm biếng

SORRY (u-u) nha

\(a,\) \(\left(3^2\right)^3\) = \(3^{2.3}\) = \(3^6\)

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

\(\left(3^2\right)^5\) = \(3^{2.5}=3^{10}\)

\(9^8=\left(3^2\right)^8=3^{2.8}=3^{16}\)

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

\(\left(5^4\right)^3=5^{4.3}=5^{12}\)

\(\left(5^2\right)^4\) = \(5^{2.4}=5^8\)

\(25^5=\left(5^2\right)^5=5^{2.5}=5^{10}\)

a, \(6^5:6^2=6^{5-2}=6^3\)

b, \(2^3.4=2^3.2^2=2^{3+2}=2^5\)

c, \(5^5:25=5^5:5^2=5^{5-2}=5^3\)

d, \(49^3:7^4=7^6:7^4=7^{6-4}=7^2\)

e, \(a^9:a=a^{9-1}=a^8\)\(\left(a\ne0\right)\)

Chúc bạn học tốt!!!

a,6⁵:6²=6^5-2=6³

b,2³x4= 2⁵

c,5⁵:25=5⁵:5⁵=1

d,49³:7⁴= 7²

e,    a⁹:a=a^9-1=a⁸

a) \(2^3=2.2.2=8\)

\(2^4=2.8=16\)

\(2^5=2.16=32\)

\(2^6=2.32=64\)

\(2^7=2.64=128\)

\(2^8=2.128=256\)

\(2^9=2.256=512\)

\(2^{10}=2.512=1024\)

b) \(4^2=4.4=16\)

\(4^3=16.4=64\)

\(4^4=64.4=256\)

Còn lại tương tự 

a) \(2^{3+4+5+6+7+8+9+10}=2^{52}\)

b) \(3^{14}\)\(=4782969\)

c) \(4^9\)\(=262144\)

d) \(5^9\)\(=1953125\)

e) \(6^9\)\(=10077696\)

K mk nha, mk nhanh nha

Bài 1 :

a) A = \(8^2\) . \(32^4\) = \(\)(2\(^3\))\(^2\) . ( \(2^5\))\(^4\) = 2\(^6\) . 2\(^{20}\) = 2\(^{26}\)

b) B = 27\(^3\) . 9\(^4\) . 243 = ( \(3^3\))\(^3\) . ( \(3^2\) )\(^4\) . 3\(^5\) = 3\(^9\) . \(3^8\) . 3\(^5\) = 3\(^{22}\)

Bài 2 : So sánh

a) A = 27\(^5\) và B =2433

Ta có : 27\(^5\) =(3\(^3\))\(^5\) = 3\(^8\) = 6561

Vì 6561 > 2433 nên A > B .

b) A = 2300 và B = 3\(^{200}\)

Ta có : B = \(3^{200}\) = 3\(^8\) . 3\(^{192}\) = 6561 . 3\(^{192}\)

Vậy chắc chắn rằng B > A .

\(25^2-24^2=49=7^2=\left(-7\right)^2\)

\(6^2-3^2=27=3^3\)

\(8^4.2^3=\left(2^3\right)^4.2^3=2^{12}.2^3=2^{15}\)

a) 25² - 24² = 625 - 576

               = 49 = 7²

b) 6² - 3² = 36 - 9

                =  27 = 3³

c) 8⁴ . 2³ = 4096 . 8

               = 32768 = 2¹⁶