To solve the equation \( 2x^{3/2} = 16 \), we can start by isolating \( x^{3/2} \).
- Divide both sides of the equation by 2:
\[ x^{3/2} = \frac{16}{2} = 8 \]
- Now, we will raise both sides to the power of \( \frac{2}{3} \) to solve for \( x \):
\[ \left(x^{3/2}\right)^{\frac{2}{3}} = 8^{\frac{2}{3}} \]
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The left side simplifies to \( x^{(3/2) \cdot (2/3)} = x^1 = x \).
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Now we need to calculate \( 8^{\frac{2}{3}} \):
\[ 8^{\frac{2}{3}} = \left(2^3\right)^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} = 2^2 = 4 \]
- Therefore, we find that:
\[ x = 4 \]
The solution to the equation \( 2x^{3/2} = 16 \) is \( x = 4 \).
So the final answer is:
\[ \boxed{4} \]