h) \( \left(\frac{1}{16}\right)^{-\frac{3}{4}}+4^{\frac{3}{4}} \cdot 8^{\frac{1}{2}} \)

To solve the expression \( \left(\frac{1}{16}\right)^{-\frac{3}{4}}+4^{\frac{3}{4}} \cdot 8^{\frac{1}{2}} \), let’s break it down step by step. First, simplify \( \left(\frac{1}{16}\right)^{-\frac{3}{4}} \): \[ \frac{1}{16} = 16^{-1} \implies \left(\frac{1}{16}\right)^{-\frac{3}{4}} = 16^{\frac{3}{4}}. \] Since \( 16 = 2^4 \), we have: \[ 16^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} = 2^{4 \cdot \frac{3}{4}} = 2^3 = 8. \] Now, simplify \( 4^{\frac{3}{4}} \cdot 8^{\frac{1}{2}} \): \[ 4^{\frac{3}{4}} = (2^2)^{\frac{3}{4}} = 2^{2 \cdot \frac{3}{4}} = 2^{\frac{3}{2}} = \sqrt{2^3} = \sqrt{8} = 2\sqrt{2}. \] And we know \( 8^{\frac{1}{2}} = \sqrt{8} = 2\sqrt{2} \). Now multiply: \[ 4^{\frac{3}{4}} \cdot 8^{\frac{1}{2}} = (2\sqrt{2})(2\sqrt{2}) = 4 \cdot 2 = 8. \] Finally, combine the results: \[ \left(\frac{1}{16}\right)^{-\frac{3}{4}} + 4^{\frac{3}{4}} \cdot 8^{\frac{1}{2}} = 8 + 8 = 16. \] Thus, the final answer is: \[ \boxed{16}. \]