Sederhanakan 81³.27²/9²=

By Admin ReiPosted on December 9, 2022

Sederhanakan 81³.27²/9²=

Sederhanakan 81³.27²/9²=

3¹⁴

− Sifat – sifat yang berlaku pada Perpangkatan, yaitu:

$: sf{a {}^{n} times a {}^{m} = a {}^{ m + n} }$
$: sf{ frac{a {}^{m} }{a {}^{n} } = a {}^{m-n} }$
$: sf{( a {}^{m} ) {}^{n} = a {}^{m times n} }$
$: sf{(a times b) {}^{n} = a {}^{n} times b {}^{n} }$
$: sf{( frac{a}{b} ) {}^{n} = frac{a {}^{n} }{b {}^{n} } }$
$sf{: a {}^{ - n} = frac{1}{a {}^{n} } }$
$: sf{a {}^{n} = frac{1}{a {}^{ - n} } }$
$: sf{a {}^{ frac{m}{n} } = sqrt[n]{a {}^{m} }}$
$: sf{a {}^{0} = 1 }$
$: sf{ - a {}^{0} = - 1 }$

$\$

Penyelesaian

Diketahui:

$frac{81 {}^{3} times 27 {}^{2} }{9 {}^{2} }$

$:$

Ditanya:

Sederhanakan ?

$:$

-Jawab:

$frac{81 {}^{3} times 27 {}^{2} }{9 {}^{2} } = ...$

$= frac{(3 {}^{4} ) {}^{3} times (3 {}^{3} ) {}^{2} }{(3 {}^{2} ) {}^{2} }$

$= frac{3 {}^{12} times 3 {}^{6} }{3 {}^{4} }$

$= 3 {}^{12 + 6 - 4}$

$= boxed{ 3 {}^{14} }$

Penjelasan dengan langkah-langkah:

$sf frac{ {81}^{3}. {24}^{2} }{ {9}^{2} }$

$sf = frac{ {( {3}^{4}) }^{3}. {( {3}^{3}) }^{2} }{ {( {3}^{2}) }^{2} }$

$sf = frac{ {3}^{12} . {3}^{6} }{ {3}^{4} }$

$sf = {3}^{12 + 6 - 4}$

$sf = {3}^{14}$

$sf = {9}^{7}$