# 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

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Expert Answers

jeew-m | Certified Educator

Consider a two positive numbers a, b and c.

Then;

`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.**