Question

Calcule as potências e dê o resultado respectivamente (em ordem) → 
$27 \frac{1}{3} \: 16 \frac{1}{2} \: 125 \frac{1}{3} \: 36 \frac{1}{2}$
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Answer 1

$27^{\frac{1}{3}}=\sqrt[3]{27} =3\\\\16^{\frac{1}{2}}=\sqrt[]{16} =4\\\\125^{\frac{1}{3}}=\sqrt[3]{125} =5\\\\36^{\frac{1}{2}}=\sqrt[]{36} =6$

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$27^{\frac{1}{3}}=(3^3)^{\frac{1}{3}}=3^{\frac{3\cdot1}{3}} =3^{\frac{3}{3}}=3^1=3\\\\16^{\frac{1}{2}}=(2^4)^{\frac{1}{2}}=2^{\frac{4\cdot1}{2}} =2^{\frac{4}{2}}=2^2=4\\\\125^{\frac{1}{3}}=(5^3)^{\frac{1}{3}}=5^{\frac{3\cdot1}{3}} =5^{\frac{3}{3}}=5^1=5\\\\36^{\frac{1}{2}}=(6^2)^{\frac{1}{2}}=6^{\frac{2\cdot1}{2}} =6^{\frac{2}{2}}=6^1=6$

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Em ordem crescente

$27^{\frac{1}{3} }<16^\frac{1}{2} < 125^{\frac{1}{3} }<36^\frac{1}{2}$