IMathAS-libretexts

Properties of Rational Functions
The notation $\displaystyle \sqrt{{{a}}}$ , is Radical Notation for the square root of $\displaystyle {a}$ The notation $\displaystyle {a}^{{\frac{{1}}{{2}}}}$ is Rational Exponent Notation for the square root of $\displaystyle {a}$ $\displaystyle {a}^{{\frac{{p}}{{q}}}}={\sqrt[{{p}}]{{{a}^{{q}}}}}={\left({\sqrt[{{p}}]{{{a}}}}\right)}^{{q}}$ The nth root of $\displaystyle {a}$ can be written as $\displaystyle {\sqrt[{{n}}]{{{a}}}}$ and as $\displaystyle {a}^{{\frac{{1}}{{n}}}}$ $\displaystyle {a}^{{\frac{{1}}{{n}}}}=\sqrt{{{a}^{{n}}}}$

Properties of Rational Functions

Below are statements about Radicals and Rational Exponents. Which of the statements are true? Check all that apply.

The notation $\displaystyle \sqrt{{{a}}}$ , is Radical Notation for the square root of $\displaystyle {a}$
The notation $\displaystyle {a}^{{\frac{{1}}{{2}}}}$ is Rational Exponent Notation for the square root of $\displaystyle {a}$
$\displaystyle {a}^{{\frac{{p}}{{q}}}}={\sqrt[{{p}}]{{{a}^{{q}}}}}={\left({\sqrt[{{p}}]{{{a}}}}\right)}^{{q}}$
The nth root of $\displaystyle {a}$ can be written as $\displaystyle {\sqrt[{{n}}]{{{a}}}}$ and as $\displaystyle {a}^{{\frac{{1}}{{n}}}}$
$\displaystyle {a}^{{\frac{{1}}{{n}}}}=\sqrt{{{a}^{{n}}}}$