Question

Put these in order starting with the smallest.

Answer 1

Answer:

${27}^{ \frac{1}{3} } < {125} ^{ \frac{2}{3} } < {9}^{ \frac{3}{2} }$

Step-by-step explanation:

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

Answer 2

Answer:

Step-by-step explanation:

$9^{\frac{3}{2} }$ = ( √9 )³ = 27

$27^{\frac{1}{3} }$ = ∛27 = 3

$125^{\frac{2}{3} }$ = ( ∛125 )² = 25

$27^{\frac{1}{3} }$ , $125^{\frac{2}{3} }$ , $9^{\frac{3}{2} }$