Roots: Fractional Exponents - Conversion Between Root and Power Form

$$\left(\sqrt[14]{49}\right)^7 = $$

Correct. [[Snippet]] Convert the root to a fractional power (the power is the top of the fraction, and the root is the bottom of the fraction). >$$\left(\sqrt[14]{49}\right)^7 = 49^{\frac{7}{14}}$$ Reduce the fractional exponent. >$$49^{\frac{7}{14}} = 49^{\frac{1}{2}}$$ Remember that an exponent of $$\frac{1}{2}$$ is the same as a square root (or you can directly convert back to a root using the above rule). >$$49^{\frac{1}{2}} = \sqrt{49} = 7$$

Incorrect. [[Snippet]]

$$\sqrt{7}$$

$$7$$

$$\sqrt{14}$$

$$14$$