why is
19x^-2
not a monomial
thank you
terms are separated by + or - signs
your expression thus has two terms, so it is a binomial
oops. My bad. I read it as 19x - 2
it is a monomial, in the strictest sense of having only one term.
But a monomial is a polynomial with only one term.
polynomials do not have negative exponents.
thank you Oobleck
A monomial is a polynomial expression that consists of only one term. In other words, it is an algebraic expression with one variable and non-negative integer exponents.
Let's examine the expression 19x^(-2). The variable x has an exponent of -2. In order for this expression to be a monomial, all exponents must be non-negative integers.
A negative exponent indicates the reciprocal of the base with a positive exponent. So, x^(-2) is equal to 1/(x^2).
Therefore, the expression 19x^(-2) can be simplified to 19/(x^2).
Since this expression involves division (19 divided by x^2), it does not meet the criteria of a monomial, which requires just one term without any division operations.
Thus, 19x^(-2) is not a monomial.