Question

Question in attachment :-

Answer 1

(4)⅓ , (5)¼ , (8)½

take LCM of { 3, 4 , 2 } = 12

so, we also write

(4)^4/12 , (5)^3/12 , (8)^6/12

so, ( 4⁴)^1/12 , ( 5³)^1/12 , (8^6)^1/12

( 256)^1/12 , ( 125)^1/12 , ( 8^6)^1/12

we know, that ,

8^6 > 256 > 125

(8^6)^1/12 > (4⁴)^1/12> (5³)^1/12

so, (8)½ > (4)⅓ > (5)¼

Answer 2

hai friend,

here is your answer,

4^1/3,5^1/4,8^1/2

taking LCM of 3,4,2

LCM of 3,4,2 is 12

so,

4^1/3=4^1/3*4/4
=4^4/12

5^1/4
=5^3/12

8^1/2=8^6/12

As all the exponents having same exponent 1/12

we will compare the bases

256, 125,8^6

so, descending order
(8^6/12)> (4^4/12) > (5^3/12)
√8 > 4^1/3 > 5*1/4

hope helped!!