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Gemiola [76]
2 years ago
10

Put these in order starting with the smallest.

Mathematics
2 answers:
elena-s [515]2 years ago
8 0

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} }

Alexxandr [17]2 years ago
7 0

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} }

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