To simplify the expression [tex]\( m^2 \cdot m^{\frac{2}{2}} \cdot m^{-2} \)[/tex], we will follow these steps:
1. Identify and simplify each exponent:
- [tex]\( m^2 \)[/tex] is already simplified.
- [tex]\( m^{\frac{2}{2}} \)[/tex] can be simplified by reducing the fraction [tex]\(\frac{2}{2} = 1\)[/tex], so it becomes [tex]\( m^1 \)[/tex].
- [tex]\( m^{-2} \)[/tex] is already simplified.
2. Combine the expressions using properties of exponents:
- When multiplying expressions with the same base, we add their exponents:
[tex]\[
m^2 \cdot m^{1} \cdot m^{-2}
\][/tex]
3. Add the exponents together:
- The exponents are [tex]\(2\)[/tex], [tex]\(1\)[/tex], and [tex]\(-2\)[/tex]:
[tex]\[
2 + 1 + (-2) = 1
\][/tex]
4. Simplify the result:
- Therefore, the simplified expression is:
[tex]\[
m^1 \quad \text{or} \quad m
\][/tex]
So, the expression [tex]\( m^2 \cdot m^{\frac{2}{2}} \cdot m^{-2} \)[/tex] in simplest form is:
[tex]\[
\boxed{m}
\][/tex]
