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

Correct.
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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.
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$$\sqrt{7}$$

$$7$$

$$\sqrt{14}$$

$$14$$