Question

Rewrite the rational exponent as a radical expression. (3^(2/3))^(1/6)

a) The sixth root of 3
b) The ninth root of 3
c) The eighteenth root of 3
d) The sixth root of 3 to the third power

Answer 1

The rational exponent (3^(2/3))^(1/6) simplifies to 3^(1/9) when multiplying the exponents. Thus, it can be expressed as the ninth root of 3, which is answer choice b).

The correct option is b.

Step-by-step explanation:

To rewrite the rational exponent (3^(2/3))^(1/6) as a radical expression, we need to apply the rules for dealing with exponents. When raising an exponent to another power, you multiply the exponents.

Here, multiplying 2/3 by 1/6 gives us 2/18, which simplifies to 1/9. Therefore, (3^(2/3))^(1/6) simplifies to 3^(1/9), which can be written as the radical expression, the ninth root of 3. So the answer is b) The ninth root of 3.

The correct option is b.