Final answer:
The expression {8x}^{4} - {5x}^{2} - 1 is a trinomial, which is a polynomial with three terms. It consists of terms with different powers of x, each term separated by a plus or minus sign.
Step-by-step explanation:
The expression {8x}^{4} - {5x}^{2} - 1 is an example of a trinomial. A trinomial is a polynomial with exactly three terms, each separated by a plus (+) or minus (-) sign. In this case, the three terms are {8x}^{4}, {5x}^{2}, and -1. A binomial would have only two terms, a monomial just one, and there is no standard mathematical term 'exponent binomial'.
To further understand the concept, we remember that exponents are used to represent repeated multiplication of a number by itself. For instance, 52 means to multiply 5 by itself, resulting in 25. In the expression provided, {8x}4 indicates the multiplication of 8x by itself four times, and {5x}2 the multiplication of 5x by itself twice.