\(12^8.9^{12}=18^{16}\)

\(\left(3.4\right)^8.3^{24}=\left(2.9\right)^{16}\)

\(3^8.4^8.3^{24}=2^{16}.9^{16}\)

\(3^{32}.2^{16}=2^{16}.3^{32}\)

Lời giải:

$12^8.9^{12}=(2^2.3)^8.(3^2)^{12}=2^{16}.3^8.3^{24}=2^{16}.3^{32}$

$=2^{16}.(3^2)^{16}=2^{16}.9^{16}=(2.9)^{16}=18^{16}$

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

         \(9^{12}=\left(9^3\right)^4=729^2\)

=> \(12^8\cdot9^{12}=144^4\cdot729^4=\left(144\cdot729\right)^4=104976^4\)(1)

Ta lại có \(18^{16}=\left(18^4\right)^4=104976^4\)(2)

Từ (1) và (2) => \(12^8\cdot9^{12}=18^{16}\)

12⁸.9¹²

= (3.2.2)⁸.(3²)¹²

= 3⁸.2⁸.2⁸.3²⁴

= 3³².2¹⁶

= (3²)¹⁶.2¹⁶

= 9¹⁶.2¹⁶

= (9.2)¹⁶

= 18¹⁶

=> đpcm.

12⁸.9¹²

=(2².3)⁸.9¹²

=(2²)⁸.3⁸.9¹²

=2¹⁶.(3²)⁴.9¹²

=2¹⁶.9⁴.9¹²

=2¹⁶.9¹⁶

=(2.9)¹⁶

=18¹⁶

12⁸.9¹²=3⁸.4⁸.9¹²=9⁴.4⁸.9¹²=9¹⁶.2¹⁶=18¹⁶

\(12^8.9^{12}=\left(2^2\right)^8.3^8.\left(3^2\right)^{12}=2^{16}.3^8.3^{24}=2^{16}.3^{32}=2^{16}.\left(3^2\right)^{16}=2^{16}.9^{16}=18^{16}\)

Vậy ta có đpcm: \(12^8.9^{12}=18^{16}\)

\(VT=12^8.9^{12}=\left(2^2.3\right)^8.\left(3^2\right)^{12}=2^{16}.3^8.3^{24}=2^{16}.3^{32}=2^{16}.\left(3^2\right)^{16}=2^{16}.9^{16}=\left(2.9\right)^{16}=18^6=VP\)

Xét: \(12^8\cdot9^{12}=\left(2^2\cdot3\right)^8\cdot\left(3^2\right)^{12}\)

\(=2^{16}\cdot3^8\cdot3^{24}=2^{16}\cdot3^{32}\)

\(=2^{16}\cdot\left(3^2\right)^{16}=2^{16}\cdot9^{16}=18^{16}\)

Ta có:

\(12^8.9^{12}=2^{16}.9^4.9^{12}=2^{16}.9^{16}=\left(2.9\right)^{16}=18^{16}\left(đpcm\right)\)

12⁸.9¹²

(2².3)⁸.9¹²

(2²)⁸.3⁸.9¹²

2¹⁶.(3²)⁴.9¹²

2¹⁶.9⁴.9¹²

2¹⁶ .9¹⁶

(2.9)¹⁶

=18¹⁶

12⁸*9¹²=3⁸*4⁸*(3²)¹²=3⁸*3^2*12*(2²)⁸=3⁸*3²⁴*2¹⁶=3³²*2¹⁶=9¹⁶*2¹⁶=(9*2)¹⁶=18¹⁶

=>đpcm

12⁸.9¹²=18¹⁶

=3⁸.4⁸.3¹².4¹²

=(3⁸.3¹²).(4⁸.4¹²)

=(3⁸⁺¹²).(4⁸⁺¹²)

=3²⁰.4²⁰

=12²⁰