Question

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Answer 1

Question :-

Simplify the following using laws of exponents.

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$\sf \dfrac{18^4\times 9^2 \times 8}{6^3 \times 16^2 \times 26}$

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Answer :-

$\sf \dfrac{18^4\times 9^2 \times 8}{6^3 \times 16^2 \times 26}$

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$\implies\sf\dfrac{ (2 \times 9)^4 \times (3^2)^2 \times 2^3}{(2\times3)^3 \times (2^4)^2 \times 3^3}$

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$\implies\sf \dfrac{ 2^4 \times 9^4 \times 3^4 \times 2^3 }{ 2^3 \times 3^3 \times 2^8 \times 3^3 }$

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

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$\implies\sf\dfrac{ 2^4 \times 3^8 \times 3^4 \times 2^3 }{ 2^3 \times 3^3 \times 2^8 \times 3^3 }$

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

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$\implies\sf \dfrac{2^{4+3} \times 3^{8+4}}{2^{3+8} \times 3^{3+3}}$

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$\implies\sf\dfrac{2^7 \times 3^12}{ 2^{11} \times 3^9}$

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$\implies\sf 2^{7-11} \times 3^{12-9}$

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$\implies\sf 2^{-4} \times 3^3$

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$\implies\sf\dfrac{3^3}{2^4}$

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$\implies\boxed{\sf \dfrac{27}{16}}$

Answer 2

$\huge\sf\color{purple}\underline{\underline{Question}} :$

$\sf \dfrac{18^4\times 9^2 \times 8}{6^3 \times 16^2 \times 26}$

$\huge\sf\color{purple}\underline{\underline{Answer}} :$

$\large \sf \bf ☞ \frac{3³}{2⁴}= \frac{27}{16}$

$\huge\sf\color{purple}\underline{\underline{Solution}} :$

$\implies\sf\dfrac{ (2 \times 9)^4 \times (3^2)^2 \times 2^3}{(2\times3)^3 \times (2^4)^2 \times 3^3} \\ \\ \implies\sf \dfrac{ 2^4 \times 9^4 \times 3^4 \times 2^3 }{ 2^3 \times 3^3 \times 2^8 \times 3^3} \\ \\ \implies\sf\dfrac{ 2^4 \times (3^2)^4 \times 3^4 \times 2^3 }{ 2^3 \times 3^3 \times 2^8 \times 3^3 } \\ \\ \implies\sf\dfrac{ 2^4 \times 3^8 \times 3^4 \times 2^3 }{ 2^3 \times 3^3 \times 2^8 \times 3^3 } \\ \\ \implies\sf \dfrac{(2^4 \times 2^3) \times (3^8\times 3^4)}{(2^3 \times 2^8) \times (3^3 \times 3^3 }\\ \\ \implies\sf \dfrac{2^{4+3} \times 3^{8+4}}{2^{3+8} \times 3^{3+3}} \\ \\ \implies\sf\dfrac{2^7 \times 3^12}{ 2^{11} \times 3^9} \\ \\ \implies\sf 2^{7-11} \times 3^{12-9}\\ \\ \implies\sf 2^{-4} \times 3^3\\ \\ \implies\sf\dfrac{3^3}{2^4} \\ \\ \implies\boxed{\sf \color{red} \dfrac{27}{16}}$