Which of the two is smaller - 513 or 614?

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Which of the two is smaller - $5^{\frac{1}{3}}$ or $6^{\frac{1}{4}}$ ?

Answer: Option B
:
B

Take a common power. 12 is the LCM of 3 and 4.

So $[5^{\frac{1}{3}}]^{12}$ and $[6^{\frac{1}{4}}]^{12}$

This gives $5^{4} = 625$ and $6^{3} = 216.$ Therefore $5^{\frac{1}{3}}$ > $6^{\frac{1}{4}}$ .

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