### Instruction: Evaluate $$64^{1/2}\cdot27^{-1/3}\cdot16^{1/4}.$$.### Response: To evaluate this expression, I need to simplify the powers of 64, 27, and 16 using the rules of exponents.
I also need to remember that a negative exponent means taking the reciprocal of the base, and that a fractional exponent means taking the root of the base.
[* with equations] So, $$64^{1/2}=\sqrt{64}=8,$$ $$27^{-1/3}=\frac{1}{\sqrt[3]{27}}=\frac{1}{3},$$ and $$16^{1/4}=\sqrt[4]{16}=2.$$