Question

[Hen]

Please explain
6•(1/108)^(1/6)=2^(2/3)• 3^(1/2)
How to simplify into irrational/rational exponents
Thank you
(Such as in this example)

 

[Deleted member 4993]

Please explain
6•(1/108)^(1/6)=2^(2/3)• 3^(1/2)
How to simplify into irrational/rational exponents
Thank you
(Such as in this example)

Do you know how to accomplish "prime" factorization?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Hen]

Thank you. I understand.

 

[HallsofIvy]

6 is trivially 2(3) and seeing that all bases except 108 are 2 and 3 (which are prime numbers), I would immediately think of factoring 108. 108 is even so obviously 108= 2(54). Then 54= 2(27) so 108= 2^2(27). But 27 is 3^3 so 108= (2^2)(3^3). Now write every thing in powers of 2 and 3 (there are NO irrational exponents in this problem and the only rational exponents are integers).