To solve the equation \( 2x^{3/2} = 16 \), we can follow these steps:
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Isolate the term with \( x \): \[ x^{3/2} = \frac{16}{2} = 8 \]
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Eliminate the rational exponent: To remove the exponent of \( \frac{3}{2} \), raise both sides to the reciprocal, which is \( \frac{2}{3} \): \[ x = 8^{\frac{2}{3}} \]
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Calculate \( 8^{\frac{2}{3}} \): We can express 8 as \( 2^3 \): \[ 8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} = 2^2 = 4 \]
Thus, the solution to the equation \( 2x^{3/2} = 16 \) is: \[ \boxed{4} \]
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