To find the value of [tex]\( a \)[/tex] given that the degree of the monomial [tex]\( 3x^2 y^a z^a \)[/tex] is 10, let's follow these steps:
1. Understand the definition of the degree of the monomial:
The degree of a monomial is the sum of the exponents of all the variables in the monomial.
2. Identify the exponents in the monomial [tex]\( 3x^2 y^a z^a \)[/tex]:
- The exponent of [tex]\( x \)[/tex] is 2.
- The exponent of [tex]\( y \)[/tex] is [tex]\( a \)[/tex].
- The exponent of [tex]\( z \)[/tex] is [tex]\( a \)[/tex].
3. Set up the equation for the sum of the exponents:
Since the degree of the monomial is given as 10, we add up the exponents and set the sum equal to 10:
[tex]\[
2 + a + a = 10
\][/tex]
4. Simplify the equation:
Combine like terms:
[tex]\[
2 + 2a = 10
\][/tex]
5. Solve for [tex]\( a \)[/tex]:
Subtract 2 from both sides of the equation:
[tex]\[
2a = 8
\][/tex]
Divide both sides by 2:
[tex]\[
a = 4
\][/tex]
Therefore, the value of [tex]\( a \)[/tex] is [tex]\( \boxed{4} \)[/tex].
