Using the properties of exponents to generate an equivalent expression of the following would be the rational exponent on an expression equivalent to ^3 square root 216

Answer 1

To express the cube root of 216 using rational exponents, we can write the cube root in terms of an exponent.

The cube root of a number is expressed as raising that number to the power of \( \frac{1}{3} \). Therefore, the cube root of 216 can be expressed as:

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

Thus, the equivalent expression with a rational exponent for the cube root of 216 is:

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