Question

(9^1/3 * 27^-1/2) / (3^1/6 * 3^-2/3)

Answer 1

Answer:

Solution

(9^1/3 * 27^-1/2)/(3^1/6 * 3^-2/3)

(3^2/3 * 3^-3/2)/(3^1/6*3^-2/3)

Use property with same base

a^x * a^y = a^(x+y)

(3^{2/3 -3/2}) /(3^{1/6 -2/3)

Now Take LCM of

(3^{[4-9]/6}) /(3^{[3-12]/18})

(3^{-5/6}) /(3^{-9/18})

(3^{-5/6}) /(3^{-1/2})

Use property

x^a/x^b = x^(a-b)

(3^{-5/6 - 1/2})

(3^{[-10-6]/12})

(3^{-16/12})

(3^{-4/3})

or

1/(3^{4/3})

Hopefully you got it.