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(12power4×9power4×4power2)/(6power4×8power4×3power4)

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$\\\frac{12^4\times9^4\times4^2}{6^2\times8^4\times3^4}=\frac{(3\times4)^4\times(3^2)^4\times4^2}{(3\times2)^2\times(2^3)^4\times3^4}\\\\=\frac{3^4\times3^8\times4^4\times4^2}{3^2\times3^4\times2^2\times2^{3\times4}}=\frac{3^4\times3^8\times4^4\times4^2}{3^2\times3^4\times2^2\times2^{12}}\\\\\text{We know that }(a^m)^n=a^{mn}\ also\ a^{m}\times a^n=a^{m+n}\text{ using this}\\\\\frac{3^4\times3^8\times4^4\times4^2}{3^2\times3^4\times2^2\times2^{12}}=\frac{3^{4+8}\times(2^2)^4\times(2^2)^2}{3^{4+2}\times2^{12+2}}\\\\=\frac{3^{12}\times(2^8)\times(2^4)}{3^{6}\times2^{14}}=\frac{3^{12}\times2^{12}}{3^{6}\times2^{14}}\\\\\text{ now using}\frac{a^m}{a^n}=a^{m-n}\\\\\frac{3^{12}\times2^{12}}{3^{6}\times2^{14}}=3^{12-6}2^{12-14}=3^6\times2^{-2}$

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Safeer PP

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