If t and w are positive numbers and t^9/t^2=w^12, then w^8/w^2= 1) t^2 2) t^3 3) t^4 4) t^6 5) t^12  

Expert Answers
jeew-m eNotes educator| Certified Educator

Consider a two positive numbers a, b and c.


`a^b/a^c = a^(b-c) and (a^b)^c = a^(b*c)`


In our question;

` t^9/t^2 =w^12`

`t^(9-2) = w^12`

    `t^7 = w^12`


Now `w^8/w^2 = w^(8-2) = w^6`


So we can write;

` w^12 = w^(6*2)`

      `= (w^6)^2`


`sqrt (w^12)= w^6`

   ` sqrt(t^7)= w^6`


So `w^8/W^2 = sqrt(t^7) = (t^3)*sqrtt`


So the answer is not given in the above answers.