To solve the equation \( 2x^{3/2} = 16 \), we can follow these steps:
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Isolate the \( x^{3/2} \) term: Divide both sides by 2.
\[ x^{3/2} = \frac{16}{2} = 8 \]
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Remove the exponent: To eliminate the exponent \( \frac{3}{2} \), we raise both sides to the reciprocal of \( \frac{3}{2} \), which is \( \frac{2}{3} \).
\[ x = 8^{\frac{2}{3}} \]
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Calculate \( 8^{\frac{2}{3}} \):
First, we find \( 8^{\frac{1}{3}} \):
\[ 8^{\frac{1}{3}} = 2 \]
Next, we square this result:
\[ 2^2 = 4 \]
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Final Result: Therefore, the solution for \( x \) is:
\[ x = 4 \]
Thus, the final solution to the equation \( 2x^{3/2} = 16 \) is:
\[ \boxed{4} \]
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