Question

Put these in order starting with the smallest.

Answer 1

`{27}^{ (1)/(3) } < {125} ^{ (2)/(3) } < {9}^{ (3)/(2) }`

Explanation:

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

Answer 2

Explanation:

`9^{(3)/(2) }` = ( √9 )³ = 27

`27^{(1)/(3) }` = ∛27 = 3

`125^{(2)/(3) }` = ( ∛125 )² = 25

`27^{(1)/(3) }` ,
`125^{(2)/(3) }` ,
`9^{(3)/(2) }`