Question

12⁴×9⁴×4/6³×8²×27 simplify and write in simplified form.​

Answer 1

To find :

$\sf \: Value \: of \: \dfrac{12^4 \times 9^4 \times 4 }{6^3 \times 8^2 \times 27}$

Identity used :

$\sf \bullet \: \dfrac{a^m}{a^n} \: = \: a^{m-n}$

$\sf \bullet \: a^m \times a^n = a^{m+n}$

$\sf \bullet \: (a^m)^{n} = a^{mn}$

Solution :

$\implies \dfrac{12^4 \times 9^4 \times 4 }{6^3 \times 8^2 \times 27}$

$\implies \dfrac{(3 \times 2 \times 2)^4 \times ( {3}^{2} )^4 \times {2}^{2} }{(2 \times 3)^3 \times ( {2}^{3} )^2 \times {3}^{3} }$

$\implies \dfrac{(3)^{4} \times ( {2}^{2} )^4 \times ( {3}^{8} ) \times {2}^{2} }{ {2}^{3} \times 3^3 \times {2}^{6} \times {3}^{3} }$

$\implies \dfrac{3^{(4 + 8)} \times ( {2}^{8} ) \times {2}^{2} }{ {2}^{(3 + 6)} \times {3}^{(3 + 3)} }$

$\implies \dfrac{3^{12} \times {2}^{(8 + 2)} }{ {2}^{9} \times {3}^{6} }$

$\implies \dfrac{3^{12 } \times {2}^{10} }{ {2}^{9} \times {3}^{6} }$

$\implies 3^{(12 - 6) } \times {2}^{(10 - 9)}$

$\implies 3^{6} \times {2}$

$\implies \: 1458$

ANSWER : 1458