Final answer:
The coefficient of x¹⁴y⁹ in the expansion of (xy)²³ is 1.
Step-by-step explanation:
To find the coefficient of x¹⁴y⁹ in the expansion of (xy)²³, we need to use the Binomial Theorem. According to the Binomial Theorem, the coefficient can be found using the formula C(n, r) * a^(n-r) * b^r, where C(n, r) represents the number of combinations of choosing r from n, a represents the base of the first term, b represents the base of the second term, n represents the exponent of the first term, and r represents the exponent of the second term.
In this case, the base of the first term is x, the base of the second term is y, the exponent of the first term is 23, and the exponent of the second term is 0. Plugging in these values into the formula, we get C (23, 0) * x^ (23-0) * y^0. Since C (23, 0) = 1 and any number raised to the power of 0 is 1, the coefficient of x¹⁴y⁹ is 1.