Using the properties of exponents to generate an equivalent expression, which of the following would be the rational exponent on an expression equivalent to 3√216 ?(1 point)

Question

Responses

A) −3
negative 3

B) 3

C) −1/3
negative Start Fraction 1 over 3 End Fraction

D) 1/3

Answer 1

To convert the expression \( 3\sqrt{216} \) into an expression with a rational exponent, we can rewrite the cube root as an exponent of \( \frac{1}{3} \).

The cube root of \( 216 \) can be expressed as:

\[ 3\sqrt{216} = 216^{\frac{1}{3}} \]

So, the rational exponent on the expression equivalent to \( 3\sqrt{216} \) is \( \frac{1}{3} \).

Therefore, the correct answer is:

D) \( \frac{1}{3} \).