To simplify the expression \( 2^{3/2} \times 2^{-1/2} \) using exponent properties, we can apply the property that states \( a^m \times a^n = a^{m+n} \).
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Identify the exponents:
- The exponent of the first term is \( \frac{3}{2} \).
- The exponent of the second term is \( -\frac{1}{2} \).
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Add the exponents: \[ \frac{3}{2} + \left(-\frac{1}{2}\right) = \frac{3}{2} - \frac{1}{2} = \frac{3 - 1}{2} = \frac{2}{2} = 1 \]
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Combine the terms using the results of the exponent addition: \[ 2^{3/2} \times 2^{-1/2} = 2^{1} = 2 \]
Thus, the expression \( 2^{3/2} \times 2^{-1/2} \) is equivalent to \( 2 \).