Question

the degree of the expression (4x^5y^mz) is 10. what is the value of (m)?

(a) 2
(b) 4
(c) 5
(d) 10

Explanation:

🆕 New Concept Discovered: Degree of a Monomial
Sum of exponents of all variables

Step 1: Identify the exponents of each variable

The given expression is a single term (a monomial):

$$ 4x^5y^mz $$

We identify the exponent for each variable in the term:

• For \( x \), the exponent is \( 5 \).
• For \( y \), the exponent is \( m \).
• For \( z \), there is no written exponent, which means its implied exponent is \( 1 \) (since \( z = z^1 \)).

Step 2: Set up the equation for the degree

The degree of a monomial is the sum of the exponents of all its variables.

$$ \text{Degree} = 5 + m + 1 $$

We are given that the degree of the expression is \( 10 \):

$$ 5 + m + 1 = 10 $$

Step 3: Solve for \( m \)

Combine the constant terms on the left side:

$$ 6 + m = 10 $$

Subtract \( 6 \) from both sides to find \( m \):

$$ m = 10 - 6 $$

$$ m = 4 $$

Answer:

4