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?

Answer 1

To convert the expression \(\sqrt[3]{216}\) into an equivalent expression using rational exponents, we can use the property of exponents which states that the \(n^{th}\) root of a number can be expressed as a fractional exponent. The property can be written as:

\[ \sqrt[n]{a} = a^{\frac{1}{n}} \]

For the cube root of 216, we can express it as:

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

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