valuat \( \left(\frac{81}{16}\right)^{-1 / 4} \times 2^{-1} \)

Let’s break this down step by step. First, the expression \( \left(\frac{81}{16}\right)^{-1 / 4} \) can be rewritten as follows: \[ \left(\frac{81}{16}\right)^{-1 / 4} = \left(\frac{16}{81}\right)^{1 / 4} \] Now, we can compute \( \frac{16}{81} \) to the power of \( \frac{1}{4} \): \[ \left(\frac{16}{81}\right)^{1 / 4} = \frac{16^{1 / 4}}{81^{1 / 4}} = \frac{2}{3} \] Next, we analyze the \( 2^{-1} \): \[ 2^{-1} = \frac{1}{2} \] Now we combine these two results: \[ \left(\frac{81}{16}\right)^{-1 / 4} \times 2^{-1} = \frac{2}{3} \times \frac{1}{2} = \frac{1}{3} \] Thus, the value of \( \left(\frac{81}{16}\right)^{-1 / 4} \times 2^{-1} \) is \[ \frac{1}{3} \]