To determine the value of [tex]\( m \)[/tex] such that the degree of the term [tex]\( 4x^5 y^m z \)[/tex] is 10, let's go through the steps systematically.
1. Identify the Expression:
The given expression is [tex]\( 4x^5 y^m z \)[/tex].
2. Understand the Degree of the Term:
The degree of a term in an algebraic expression is the sum of the exponents of all variables in that term.
3. Sum of Exponents:
For the term [tex]\( 4x^5 y^m z \)[/tex]:
- The exponent of [tex]\( x \)[/tex] is 5.
- The exponent of [tex]\( y \)[/tex] is [tex]\( m \)[/tex].
- The exponent of [tex]\( z \)[/tex] is 1 (since [tex]\( z \)[/tex] is the same as [tex]\( z^1 \)[/tex]).
4. Formulate the Sum:
The sum of the exponents (the degree of the term) is given by:
[tex]\[
5 + m + 1
\][/tex]
5. Given Total Degree:
It is given that the total degree of the term is 10:
[tex]\[
5 + m + 1 = 10
\][/tex]
6. Simplify the Equation:
Combine like terms:
[tex]\[
6 + m = 10
\][/tex]
7. Solve for [tex]\( m \)[/tex]:
Subtract 6 from both sides:
[tex]\[
m = 10 - 6
\][/tex]
[tex]\[
m = 4
\][/tex]
Therefore, the value of [tex]\( m \)[/tex] that satisfies the given condition is [tex]\( 4 \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
