Express square root of cube root of $x$ in exponential form.

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Solution

To find square root of a cube root
Let the given cube root be $x^{1 / 3}$
To find square root we apply power $1 / 2$ i.e. ${(x^{1 / 3})}^{1 / 2}$
Overall we find $\sqrt[6]{x}$ or $x^{1 / 6}$

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Express square root of cube root of x in exponential form.

To find square root of a cube rootLet the given cube root be x1/3To find square root we apply power 1/2 i.e. (x1/3)1/2Overall we find 6√x or x1/6

Express square root of cube root of $x$ in exponential form.

To find square root of a cube root
Let the given cube root be $x^{1 / 3}$
To find square root we apply power $1 / 2$ i.e. ${(x^{1 / 3})}^{1 / 2}$
Overall we find $\sqrt[6]{x}$ or $x^{1 / 6}$