Question

simplify 2 into 3 ^ 4 into 2 ^ 5 divided / 9 into 4 to the power of 2​

Answer 1

Answer:

36

Step-by-step explanation:

Given : ${\sf{\ \ {\dfrac{2 \times 3^4 \times 2^5}{9 \times 4^2}}}}$

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We can write the denominator as :

$\Rightarrow{\sf{{\dfrac{2 \times 3^4 \times 2^5}{(3 \times 3) \times (2 \times 2)^2}}}}$

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$\Rightarrow{\sf{{\dfrac{2 \times 3^4 \times 2^5}{3^2 \times (2^2)^2}}}}$

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${\boxed{\sf{\red{Identity \ : \ (a^m)^n = a^{mn}}}}}$

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$\Rightarrow{\sf{{\dfrac{2 \times 3^4 \times 2^5}{3^2 \times 2^4}}}}$

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Writing the common terms together in numerator.

$\Rightarrow{\sf{{\dfrac{2 \times 2^5 \times 3^4}{3^2 \times 2^4}}}}$

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${\boxed{\sf{\red{Identity \ : \ a^m \times a^n = (a)^{m + n}}}}}$

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$\Rightarrow{\sf{{\dfrac{(2)^{1 + 5} \times 3^4}{3^2 \times 2^4}}}}$

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$\Rightarrow{\sf{{\dfrac{2^6 \times 3^4}{3^2 \times 2^4}}}}$

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${\boxed{\sf{\red{Identity \ : \ {\dfrac{a^m}{a^n}} = (a)^{m - n}}}}}$

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$\Rightarrow{\sf{(2)^{6 - 4} \times (3)^{4 - 2} }}$

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$\Rightarrow{\sf{2^2 \times 3^2}}$

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$\Rightarrow{\sf{2 \times 2 \times 3 \times 3}}$

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$\Rightarrow{\boxed{\sf{\green{36}}}}$