Rewrite the rational exponent as a radical expression.3 to the 2 over 3 power, to the 1 over 6 power

Question

subject: use the rational exponent

convert into radical expresssio

Answer 1

(3^2/3)^1/6 

• (x^A)^B = x^AB so we multiply the exponents

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

3^(2/18)

3^1/9

• x^1/y = ^y√x

3^1/9 = ⁹√3

 

The answer is ⁹√3

Answer 2

(3^(2/3))^(1/6)  When raise an exponent to an exponent you multiply  for example (2²)^3 would be 2⁶ because 2 *3=6.  So we multiply (2/3)*(1/6) and we get 1/9.  When you have a fraction as an exponent, the denominator of the exponent becomes the root and the base of the exponent goes under the radical.

 

Thus 3^1/9 would be the ninth root of 3 or ⁹ √3.