Evaluate the product of the monomial expressions 4z^5 and 2z^3. Which of the following rep… — Armed Services Vocational Aptitude Battery (ASVAB)

Evaluate the product of the monomial expressions $4z^5$ and $2z^3$ . Which of the following represents the simplified result?

The expression simplifies to

8z^8

When multiplying two monomial expressions, the numerical coefficients are multiplied together (

4 \times 2 = 8

), and the exponents of the common variable base are added together according to the product rule for exponents (

5 + 3 = 8

). This results in

8z^8

Identify the operation to be performed between the two terms.

The terms

4z^5

and

2z^3

are being multiplied.

Understanding the operation is required to apply the correct mathematical rules for coefficients and exponents.

Multiply the numerical coefficients.

4 \times 2 = 8

Coefficients in a product of monomials are multiplied together normally.

Multiply the variable parts by applying the product rule for exponents.

z^5 \times z^3 = z^{5+3} = z^8

When multiplying exponential expressions with the same base, their exponents must be added.

Combine the calculated coefficient and the variable part.

8z^8

This brings the simplified pieces together into the final term.

Operations with Variable Exponents

Question