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Answer :

Xenia168go

Answer:

Step-by-step explanation:

[tex]9^{\frac{3}{2} }[/tex] = ( √9 )³ = 27

[tex]27^{\frac{1}{3} }[/tex] = ∛27 = 3

[tex]125^{\frac{2}{3} }[/tex] = ( ∛125 )² = 25

[tex]27^{\frac{1}{3} }[/tex] , [tex]125^{\frac{2}{3} }[/tex] , [tex]9^{\frac{3}{2} }[/tex]

Watsonultra2go

Answer:

[tex] {27}^{ \frac{1}{3} } < {125} ^{ \frac{2}{3} } < {9}^{ \frac{3}{2} }[/tex]

Step-by-step explanation:

[tex] {9}^{ \frac{3}{2} } = \sqrt[2]{ {9}^{3} } = \sqrt[2]{ {3}^{6} } = { 3}^{3} \\ {27}^{ \frac{1}{3} } = \sqrt[3]{27} = \sqrt[ 3]{ {3}^{3} } = 3 \\ {9}^{ \frac{3}{2} } > {27}^{ \frac{1}{ 3} } \\ \\ {125}^{ \frac{2}{3} } = \sqrt[3]{ {125}^{2} } = \sqrt[3]{ {5}^{6} } = 25 \\ \\ 3 < 25 < {3}^{3} \\ {27}^{ \frac{1}{3} } < {125} ^{ \frac{2}{3} } < {9}^{ \frac{3}{2} }[/tex]

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