Which among $${2^{\frac{1}{2}}}$$, $${3^{\frac{1}{3}}}$$, $${4^{\frac{1}{4}}}$$, $${6^{\frac{1}{6}}}$$ and $${12^{\frac{1}{{12}}}}$$ is largest?
a) $${3^{\frac{1}{3}}}$$
b) $${4^{\frac{1}{4}}}$$
c) $${12^{\frac{1}{{12}}}}$$
d) $${2^{\frac{1}{2}}}$$
Answer: a
Explanation: LCM in power 2, 3, 4, 6, 12 is 12
We multiplied the LCM to the power of the numbers.
$${2^{\frac{{1 \times 12}}{2}}},{3^{\frac{{1 \times 12}}{3}}},{4^{\frac{{1 \times 12}}{4}}},{6^{\frac{{1 \times 12}}{6}}}{\kern 1pt} {\text{and}}\,{12^{\frac{{1 \times 12}}{{12}}}}$$
We get,
= 26, 34, 43, 62, 12
= 64, 84, 64, 36, 12
Hence, greatest number would be $${3^{\frac{1}{3}}}$$
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