Question 30
The value of $$\frac{\sqrt[4]{27\cdot\sqrt[3]{9}}}{\sqrt[6]{9\cdot 3^3\cdot\sqrt{3}}}$$ is ______.
Correct Answer: 1
Solution
The numerator is $$\sqrt[4]{3^3\cdot 3^{2/3}}=3^{11/12}$$. The denominator is $$\sqrt[6]{3^2\cdot 3^3\cdot 3^{1/2}}=3^{11/12}$$. Their ratio is therefore $$1$$.
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