Quiz.

By Admin ReiPosted on October 29, 2022

$( {2}^{999} + {2}^{999} ) div {( {( {16}^{12} })^{ frac{1}{2}) } }^{25} = {2}^{x}$

x = ….??

………..

Quiz.

Penjelasan dengan langkah-langkah:

$(2 {}^{999} + 2 {}^{999} ) div ((16 {}^{12} ) {}^{ frac{1}{2} } ) {}^{25} = 2 {}^{x}$

$2 times 2 {}^{999} div (16 {}^{6} ) {}^{25} = 2 {}^{x}$

$2 times 2 {}^{999} div 16 {}^{150} = 2 {}^{x}$

$2 times 2 {}^{999} div 2 {}^{600} = 2 {}^{x}$

$2 {}^{400} = 2 {}^{x}$

$2 {}^{x} = 2 {}^{400}$

$x = 400$

Jawaban:

Operasi perpangkatan

$begin{gathered}a) : a {}^{m} times a {}^{n} = a {}^{m + n} \ b) : a {}^{m} div a {}^{n} = a {}^{m - n} \ c) : (a {}^{m} ) {}^{n} = (a) {}^{m times n} \ d) : (a times b) {}^{m} = a {}^{m} times a {}^{m} \ e) : ( frac{a}{b} ) {}^{m} = frac{a {}^{m} }{b {}^{m} } end{gathered}$

$( {2}^{999} + {2}^{999} ) div {( {( {16}^{12} })^{ frac{1}{2}) } }^{25} = {2}^{x}$

$2 times 2 {}^{999}$

$((16 {}^{12} ) {}^{ frac{1}{2} }) {}^{25} = (16) {}^{12 times frac{1}{2} } ) {}^{25} \ = (16) {}^{ frac{12}{2} } ) {}^{25} \ = (16 {}^{6} ) {}^{} {}^{25} \ = (16) {}^{6 times 25} \ = 16 {}^{150}$

$= 2 times 2 {}^{999} div 16 {}^{150}$

$= 2 times 2 {}^{999} div (4 times 4) {}^{150}$

$= 2 times 2 {}^{999} div 4 {}^{150} times 4 {}^{150}$

$= 2 times 2 {}^{999} div (2 times 2) {}^{150} times (2 times 2) {}^{150}$

$= 2 times 2 {}^{999} div (2 {}^{150} times 2 {}^{150} times 2 {}^{150} times 2 {}^{150} )$

$= 2 times 2 {}^{999} div 2 {}^{(150 + 150 )+ (150 + 150)}$

$= 2 times 2 {}^{999} div 2 {}^{300 + 300}$

$= 2 times 2 {}^{999} div 2 {}^{600}$

$= 2 times 2 {}^{999 - 400}$

$= 2{}^{1} times 2 {}^{399}$

= 2³⁹⁹ + ¹

= 2⁴⁰⁰