Final answer:
The monomials that are perfect squares are B) 9x⁸, D) 25x¹², and E) 36x¹⁶, as both their coefficients and exponents form perfect squares.
Step-by-step explanation:
To determine which monomials are perfect squares, you must look at both the coefficient and the variable part. A monomial is a perfect square if it can be expressed as the square of another monomial, that is, as (axⁿ)² = a²x^(2n). Thus, both the coefficient 'a' and the exponent 'n' must form perfect squares.
B) 9x⁸ is a perfect square because 9 is a perfect square (3^2) and the exponent 8 is an even number, which is also a perfect square (2⁴).
D) 25x¹² is a perfect square because 25 is a perfect square (5²) and 12 is an even number, which is a perfect square (2⁶).
E) 36x¹⁶ is a perfect square because 36 is a perfect square (6²) and 16 is an even number, which is a perfect square (2⁸).
Options A) and C) are not perfect squares because in A) the exponent of x is not even, and in C) the coefficient is not a perfect square (16 is a perfect square but the exponent 9 is not an even number).