Let's go through the "Practice Identifying Monomials" exercise in the image step-by-step.

Part 1: Why are the following expressions not monomials?

1. 3cd⁴:

   • Reason: This is a monomial because it consists of a single term with variables raised to whole number powers. However, if you're supposed to identify non-monomials, this shouldn't be chosen.

2. x + 2w:

   • Reason: This is not a monomial because it has two terms (x and 2w), making it a binomial.

3. 3/h:

   • Reason: This is not a monomial because division by a variable (h in the denominator) is not allowed in a monomial. Monomials cannot have variables in the denominator.

4. ab⁻¹:

   • Reason: This is not a monomial because of the negative exponent (b⁻¹). In monomials, exponents must be non-negative integers.

Part 2: Which expressions are monomials?

1. −4 + 6:

   • Reason: This is not a monomial because it has two terms, making it a binomial.

2. b + 2b + 2:

   • Reason: This is not a monomial because it also has multiple terms (making it a trinomial).

3. (x − 2x)²:

   • Reason: This simplifies to 0², which is 0. Since 0 is a valid monomial, this is technically a monomial.

4. rs/t:

   • Reason: This is not a monomial because it has a variable (t) in the denominator.

5. 36x²yz³:

   • Reason: This is a monomial because it consists of a single term with variables raised to non-negative integer exponents.

6. a²:

   • Reason: This is a monomial because it's a single term with a variable raised to a non-negative integer exponent.

7. 1/x³:

   • Reason: This is not a monomial because there is a variable in the denominator.

Do you need further details or have any questions?

Here are five related questions to help reinforce this concept:

1. Can a constant (like 7) be considered a monomial?
2. Is a term with fractional exponents still a monomial?
3. What is the difference between a monomial and a polynomial?
4. How would you classify the expression $4a^2b^{-3}$?
5. Can you simplify $2x^3y^2 + 3x^3y^2$ to form a monomial?

Tip: Always check if a term has only non-negative integer exponents and no variables in the denominator to identify a monomial.