Question

simplify - 12 power 4 * 9 power 3 * 4 upon 6 power 3 * 8 power 2 * 27

Answer 1

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Answer 2

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

Step-by-step explanation:

Given : Expression $\dfrac{12^4\times 9^3\times 4}{6^3\times 8^2\times 27}$

To find : Simplify the expression ?

Solution :

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

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

$=\dfrac{ {3}^{4}\times{2}^{4} \times {2}^{4} \times {3}^{3} \times {3}^{3} \times {2}^{2} }{ {2}^{3} \times {3}^{3}\times{2}^{2}\times{2}^{2}\times {2}^{2} \times {3}^{3}}$

Using the identity,

${a}^{m} \times{a}^{n}= {a}^{m + n}$

$= \dfrac{ {2}^{4 + 4 + 2}\times{3}^{4 + 3 + 3}}{{2}^{3+2+2 + 2} \times {3}^{3 + 3}}$

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

Using the identity,

$\frac{ {a}^{m} }{{a}^{n}}= {a}^{m - n}$

$={2}^{10 - 9} \times {3}^{10 - 6}$

$={2}^{1}\times {3}^{4}$

$= 2\times {3}^{4}$

Therefore, $\dfrac{12^4\times 9^3\times 4}{6^3\times 8^2\times 27}=2\times {3}^{4}$

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