\root(k)(x^(p)) rewrit using a rational expression show all your work

Answer 1

To rewrite the expression $\sqrt[k]{x^p}$ using a rational expression, we can rewrite the square root as a fractional exponent:

$\sqrt[k]{x^p} = (x^p)^{1/k}$

Then, we can simplify this further using the properties of exponents:

$(x^p)^{1/k} = x^{p/k}$

Therefore, $\sqrt[k]{x^p}$ can be expressed as $x^{p/k}$, which is a rational expression.