Question

Find the median of (27)^2/3,
(32)^3/5 and (625)^3/4.
Explain step by step.​

Answer 1

Answer:

Required median of  ( 27 )^( 2 / 3 ) , ( 32 )^( 3 / 5 ) and ( 625 )^( 3 / 4 ) is ( 27 )^( 2 / 3 ).

Step-by-step explanation:

We have to find the median of ( 27 )^( 2 / 3 ) , ( 32 )^( 3 / 5 ) and ( 625 )^( 3 / 4 ).

First of all, simplifying the given terms.

= > ( 27 )^( 2 / 3 ) = { 3 x 3 x 3 }^( 2 / 3 )

= > ( 27 )^( 2 / 3 ) = { 3^3 }^( 2 / 3 )

= > ( 27 )^( 2 / 3 ) = 3^( 3 x 2 / 3 )

= > ( 27 )^( 2 / 3 ) = 3^2

= > ( 27 )^( 2 / 3 ) = 9

= > ( 32 )^( 3 / 5 ) = { 2 x 2 x 2 x 2 x 2 }^( 3 / 5 )

= > ( 32 )^( 3 / 5 ) = { 2^5 }^( 3 / 5 )

= > ( 32 )^( 3 / 5 ) = { 2 }^( 5 x 3 / 5 )

= > ( 32 )^( 3 / 5) = 2^3

= > ( 32 )^( 3 / 5 ) = 8

= > ( 625 )^( 3 / 4 ) = { 5 x 5 x  5 x 5 }^( 3 / 4 )

= > ( 625 )^( 3 / 4 ) = { 5^4 }^( 3 / 4 )

= > ( 625 )^( 3 / 4 ) = 5^( 4 x 3 / 4 )

= > ( 625 )^( 3 / 4 ) = 5^3

= > ( 625 )^( 3 / 4 ) = 125

Terms are 9 , 8 , 125( in simplest form ). Now it is clearly visible that the median is 9{ since 9 > 8 , also , 9 < 125 } .

Hence the required median of  ( 27 )^( 2 / 3 ) , ( 32 )^( 3 / 5 ) and ( 625 )^( 3 / 4 ) is 9 or ( 27 )^( 2 / 3 ).

Answer 2

We know that:

(27)^2/3 = {(3)^3}^2/3

=(3)^2

=9

And,

(32)^3/5 = {(2)^5}^3/5

=(2)^3

=8

Also, (625)^3/4 ={(5^4)^3/4}

=(5)^3

=125

Now the mean of (27)^2/3,(32)^3/5 and (625)^3/4 is the same as that of 9, 8, and 125

That is:-

(9+8+125) / 3

= 142/3

=47.3333.....