What is the value of \(27^{\frac{2}{3}}\times16^{-\frac{1}{4}}\div81^{-\frac{1}{2}}\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 40.5
In \(a^{\frac{m}{n}}\), the denominator \(n\) gives the root and the numerator \(m\) the power; a negative power means the reciprocal.
\(27^{\frac{2}{3}}=(\sqrt[3]{27})^{2}=3^{2}=9\)
\(\displaystyle16^{-\frac{1}{4}}=\frac{1}{\sqrt[4]{16}}=\frac{1}{2}\)
\(\displaystyle81^{-\frac{1}{2}}=\frac{1}{\sqrt{81}}=\frac{1}{9}\)
\(\displaystyle9\times\frac{1}{2}\div\frac{1}{9}=\frac{9}{2}\times9=\frac{81}{2}=40.5\)