2x^1/2×3x^-5/2

To simplify the expression \( 2x^{1/2} \times 3x^{-5/2} \), you can follow these steps:

1. Multiply the constants (coefficients): \[ 2 \times 3 = 6 \]

2. Add the exponents of \(x\) (since the bases are the same): \[ x^{1/2} \times x^{-5/2} = x^{1/2 + (-5/2)} = x^{-4/2} = x^{-2} \]

3. Combine the results: \[ 6x^{-2} \]

4. Expressing with positive exponent (if desired): \[ 6x^{-2} = \frac{6}{x^2} \]

Thus, the simplified expression is: \[ \frac{6}{x^2} \]