How do I write this question, 2^1/3 in the radical form?

Question

anonymous · Answer

$$^3\sqrt{2}$$

anonymous · Answer

If your exponent is a fraction, the denominator is the root and the numerator is the number outside of your root.

anonymous · Answer

In general the relationship between rational exponent and radical is$$x ^{\frac{m}{n}}=\sqrt[n]{x^m}$$

anonymous · Answer

as long as n != 0

anonymous · Answer

what if n < 0?

anonymous · Answer

yes you are correct!

anonymous · Answer

Oh how about if the exponent is negative? Such as: 7^-1/2?

anonymous · Answer

negative exponent means reciprocal regardless if the exponent is integer, rational or real.

anonymous · Answer

so you mean, the negative exponent would be 2/1?

anonymous · Answer

$$7^{-1/2}=\frac{1}{7^{1/2}}$$

anonymous · Answer

reciprocal with respect to the base, not the exponent

anonymous · Answer

ohhh, thank you!

anonymous · Answer

You do know that in radical form, a radical in the denominator is not considered simplified.  If you are in a class below calculus, you will have to "rationalize" the denominator.

anonymous · Answer

$$=\frac{1}{\sqrt{7}}*\frac{\sqrt{7}}{\sqrt{7}}=\frac{\sqrt{7}}{7}$$