Which of the two is smaller - 513 or 614?

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Question

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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