Question

Create your own term using a rational exponent and then convert it to a radical expression. Explain, in complete sentences, how the expression was converted. :]

Answer 1

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

Answer 2

In general \[x^{a/b}=\sqrt[b]{x^{a}}\]. Rational means ratio or fraction. You can raise some number, x, to any fraction such as \[23^{4/7}\]. The exponent here is the fraction \[4/7\]. This means 23 needs to be raised to the fourth power and then the seventh root is taken (or vice versa). When the switch is made to radical notation then the denominator is placed in the "crook" of the radical sign and the numerator will go under the radical as a conventional exponent. Both terms means the same thing they are just different ways to write it.

Answer 3

thanks :]