To simplify the expression [tex]\( m^2 \cdot m^{\frac{3}{2}} \cdot m^{-2} \)[/tex], we follow the rules of exponents. Specifically, when we multiply expressions with the same base, we add their exponents.
Let's begin by rewriting the exponents of the given expression:
- The exponent of the first term is [tex]\( 2 \)[/tex].
- The exponent of the second term is [tex]\( \frac{3}{2} \)[/tex].
- The exponent of the third term is [tex]\( -2 \)[/tex].
To simplify the expression, we add these exponents together:
[tex]\[ 2 + \frac{3}{2} - 2 \][/tex]
Next, we perform the addition:
1. [tex]\( 2 - 2 = 0 \)[/tex]
2. [tex]\( 0 + \frac{3}{2} = \frac{3}{2} \)[/tex]
So, the combined exponent is [tex]\( \frac{3}{2} \)[/tex].
Thus, the expression [tex]\( m^2 \cdot m^{\frac{3}{2}} \cdot m^{-2} \)[/tex] simplifies to:
[tex]\[ m^{\frac{3}{2}} \][/tex]
The simplest form of the expression is:
[tex]\[ m^{\frac{3}{2}} \][/tex]
