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 cubed.

Answer 1

To rewrite the rational exponent 3^(2/3)^(1/6) as a radical expression, we need to determine the equivalent radical expression. The expression 3^(1/3) represents the cube root of 3.

Step-by-step explanation:

To rewrite the rational exponent 3^(2/3)^(1/6) as a radical expression, we need to determine the equivalent radical expression.

First, we can rewrite the rational exponent as a single fraction, by multiplying the exponents: 3^((2/3)(1/6)).

Next, we can simplify the exponent by multiplying the numerators and denominators of the fractions to get: 3^(1/3).

Finally, the expression 3^(1/3) represents the cube root of 3.