Write \( 3 \sqrt{10} \) using rational exponents

To express \( 3 \sqrt{10} \) using rational exponents, we first recognize that the square root can be rewritten as an exponent. Specifically, the square root of 10 can be expressed as \( 10^{1/2} \). Therefore, we have: \[ 3 \sqrt{10} = 3 \times 10^{1/2} \] In this case, \( 3 \) remains as a coefficient, and \( \sqrt{10} \) is represented as \( 10^{1/2} \). So, the final expression is: \[ 3 \sqrt{10} = 3 \times 10^{1/2} \]