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

3
3

−3
negative 3

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

1/3
Start Fraction 1 over 3 End Fraction

Answer 1

To convert the expression \( 3\sqrt{216} \) into an expression with a rational exponent, we first express the cube root as an exponent. The cube root can be written as raising to the power of \( \frac{1}{3} \). Therefore, we can rewrite the expression as:

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

Since this is equivalent to \( 216^{1/3} \), we see that the rational exponent is:

\[ \frac{1}{3} \]

Thus, the correct response is:

\(\frac{1}{3}\) (Start Fraction 1 over 3 End Fraction).