SOLUTION: Solve this: (9x^6*y^8)^(1/6) And I have this possible answers a. xy(9y8)^(1/6) b. xy(3y)^(1/3) c. 3xy d. x(9y^2)^(1/6)

Solve this:
(9x6y8)1/6

And I have this possible answers

a. xy(9y8)1/6
b. xy(3y)1/3 <------- that's the answer!
c. 3xy
d. x(9y2)1/6

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(9x6y8)1/6

Write the 9 as 32 

(32x6y8)1/6


Remove the parentheses by multiplying each inner exponent by the
outer exponent 1/6

3(2)(1/6)x(6)(1/6)y(8)(1/6)

32/6x6/6y8/6

Reduce the fraction exponents

31/3x1y4/3

Change improper fraction exponent 4/3 to 1 1/3 but write it as 1+1/3

31/3x1y1+1/3

Now since we add exponents of like bases to multiply, we can use that 
fact in reverse, and when we see an exponent consisting of an addition,
such as in y1+1/3 we can write that as the multiplication y1y1/3.

31/3x1y1y1/3

Now we put the two factors which have the same exponent 1/3 together

31/3y1/3x1y1

Now since to remove parentheses we multiply the inner exponents by the
outer exponents, we can use that fact in reverse to say that when two
factors have the same exponents, we can put the product of the bases
inside parentheses and use the common exponent outside the parentheses,
so 31/3y1/3 can be written as (3y)1/3

So the above becomes

(3y)1/3x1y1

We can erase the 1 exponents and get

(3y)1/3xy

which is the same as

xy(3y)1/3

which is answer b.

Edwin
AnlytcPhil@aol.com