Question Given that the meaning of a rational exponent can be connected to the meaning of a root, how can you rewrite ^3√5using a rational exponent?

Answer 1

The expression \( \sqrt[3]{5} \) can be rewritten using a rational exponent as follows:

\[ \sqrt[3]{5} = 5^{1/3} \]

In general, the \( n \)-th root of a number \( a \) can be expressed as \( a^{1/n} \). Therefore, the cube root (third root) of 5 is written as \( 5^{1/3} \).