To simplify the given expression \((36x^4y^5) / ((3xy)^2)\), we first simplify the denominator \((3xy)^2\):
\[ (3xy)^2 = (3^2)(x^2)(y^2) = 9x^2y^2 \]
Now we can rewrite the original expression:
\[ \frac{36x^4y^5}{9x^2y^2} \]
Next, we simplify the fraction by dividing both the numerator and the denominator by their common factors:
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Numerical Coefficient: \[ \frac{36}{9} = 4 \]
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For \(x\) terms: \[ \frac{x^4}{x^2} = x^{4-2} = x^2 \]
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For \(y\) terms: \[ \frac{y^5}{y^2} = y^{5-2} = y^3 \]
Now, putting it all together, we have:
\[ \frac{36x^4y^5}{9x^2y^2} = 4x^2y^3 \]
Thus, the simplified expression is:
\[ 4x^2y^3 \]
So the expression \( (36x^4 y^5) / ((3xy)^2) \) simplifies to \( 4x^2y^3 \), which corresponds to option Η.