Question
valuat \( \left(\frac{81}{16}\right)^{-1 / 4} \times 2^{-1} \)
Ask by Bates Collins. in Nigeria
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value is \( \frac{1}{3} \) or \( 0.\dot{3} \).
Solution
Calculate or simplify the expression \( (81/16)^{-1/4} * 2^{-1} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}\)
- step1: Rewrite the fraction:
\(\left(\frac{81}{16}\right)^{-\frac{1}{4}}\times 2^{-1}\)
- step2: Multiply the terms:
\(81^{-\frac{1}{4}}\)
- step3: Express with a positive exponent:
\(\frac{1}{81^{\frac{1}{4}}}\)
- step4: Evaluate the power:
\(\frac{1}{3}\)
The value of \( \left(\frac{81}{16}\right)^{-1 / 4} \times 2^{-1} \) is \( \frac{1}{3} \) or \( 0.\dot{3} \).
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Simplify this solution Mind Expander
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 \[ \frac{1}{3} \]
