4^(1/3) * 8^(4/15) * 16^(1/20) * 32^(1/15) = ? here ^ is for powers

M4maths Previous Puzzles

06 Apr 2012 powers

4^(1/3) * 8^(4/15) * 16^(1/20) * 32^(1/15) = ?
here ^ is for powers

OPtion

1) 1
2) 2
3) 4
4) 8
5) 16
6) 2^(1/2)
7) 8^(1/2)
8) 32
9) 32^(1/2)
10) none of these

Solution

on solving we will get
2^(2/3) * 2^(12/15) * 2^(4/20) * 2^(5/15)
= 2^(2/3 + 4/5 + 1/5 + 1/3)
= 2^2 = 4

Correct Option: 3 Best Solution (16)

Dr.Dipin Singh   12 years AGO

4^(1/3) * 8^(4/15) * 16^(1/20) * 32^(1/15)
= 2^(2/3) * 2^(12/15) * 2^(4/20) * 2^(5/15)
= 2^(2/3) * 2^(4/5) * 2^(1/5) * 2^(1/3)
= 2^(2/3) * 2^(1/3)* 2^(4/5) * 2^(1/5)
= 2^1*2^1 = 2*2=4 ... option 3

Like? Yes (6) | No   

dineshv   12 years AGO

2^(2/3)*2^(12/15)*2^(4/20)*2^(5/15)

2^((2/3)+(4/5)+(1/5)+(1/3))

2^2

4

Like? Yes (3) | No   

Shiv Kumar   12 years AGO

2^(2/3)*2^(12/15)*2^(4/20)*2^(5/15)
=2^(2/3+4/5+1/5+1/3)
=2^(1+1)
=4

Like? Yes (3) | No (2)  

Viru Sihag   12 years AGO

convert all these in power of 2.
then 2^(2/3)*2^(4/5)*2^(1/5)*2^(1/3) = 2^2 = 4

Like? Yes (3) | No (2)  

Arneet   12 years AGO

4^(1/3) * 8^(4/15) * 16^(1/20) * 32^(1/15) =
2^( 2/3 +12/15 + 4/20 + 5/15) = 2^2 =4

Like? Yes (1) | No   

Suresh Varma P   12 years AGO

4 = 2^2
8 = 2^3
16 = 2^4
32 = 2^5
2^(2/3)*2^(4/5)*2^(1/5)*2^(1/3)
2^(2/3+4/5+1/5+1/3) = 2^2 = 4
Ans: option 3

Like? Yes (1) | No   

prithviraj sanningannavar   12 years AGO

4^(1/3) * 8^(4/15) * 16^(1/20) * 32^(1/15)
=2^(2/3) * 2^(12/15) * 2^(4/20) * 2^(5/15)
=2^[(2/3)+(12/15)+(4/20)+(5/15)]
=2^2
=4

Like? Yes (1) | No   

J.P.Anitha   12 years AGO

=> 4^(0.333)*8^(0.2666)*16^(0.05)*32^(0.066) => 1.58666*1.74085*1.14869*1.25701 => 3.99 (or) 4 => Ans : 4 (Option : 3)

Like? Yes (2) | No (1)  

gurumoorthy   12 years AGO

2^(2/3) * 2^(4/5) * 2^(1/5) * 2^(1/3)
2^1 * 2^1= 4

Like? Yes (1) | No   

parul mishra   12 years AGO

option (3) all the values in eq are in the base of 2
2^2^1/3=4^1/3
2^3^4/15=8^4/15
2^4^1/20=16^1/20
2^5^1/15=32^1/15
now base is same as 2 powers can be added so
2^(2/3+4/5+1/5+1/3)=2^2=4

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vignesh waran A   12 years AGO

Convert all the numbers into powers of 2 by simplification we get ans. As 4

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SEDHUPATHY S   12 years AGO

4^(1/3) * 8^(4/15) * 16^(1/20) * 32^(1/15)
-> (2*2)^(1/3)*(2*2*2)^(4/15)*(2*2*2*2)^(1/20)*(2*2*2*2*2)^(1/15)
-> (2^2)^(1/3)*(2^3)^(4/15)*(2^4)^(1/20)*(2^5)^(1/15)
-> 2^(2/3+4/5+1/5+1/3)
-> 2^2
-> ANS: 4 , option:3

Like? Yes (1) | No   

Balakrishnan M   12 years AGO

4^(1/3)*8^(4/15)*16^(1/20)*32^(1/15)
=(2^2)^(1/3)*(2^3)^(4/15)*(2^4)^(1/20)*(2^5)^(1/15)
=2^(2/3)*2^(12/15)*2^(4/20)*2^(5/15)

Like? Yes (1) | No   

Amit kumar   12 years AGO

2^(2/3)*2^(4/5)*2^(1/5)*2^(1/3)
=2^(1+1)
=2^2
=4

Like? Yes (1) | No   

Vivek Yadav   12 years AGO

convert all base into 2...
2^(2/3)*2^(4/5)*2^(1/5)*2^(1/3)=2^(2/3+4/5+1/5+1/3) =2^2=4.

Like? Yes (2) | No (1)  

sridhar reddy   12 years AGO

on simplifying
2^[(2/3)+(4/5)+(1/5)+(1/3)]
=2^2
=4

Like? Yes (2) | No (1)