sqrt[4]{sqrt[3]{2^{2}}} equals | vedclass

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Question

(B) To solve the expression $\sqrt[4]{\sqrt[3]{2^{2}}}$,we use the laws of exponents.First,express the radicals as fractional exponents: $\sqrt[n]{x}

Vedclass · Accepted Answer

$2^{\frac{1}{6}}$

Vedclass · Answer

(B) To solve the expression $\sqrt[4]{\sqrt[3]{2^{2}}}$,we use the laws of exponents.First,express the radicals as fractional exponents: $\sqrt[n]{x} = x^{\frac{1}{n}}$.$\sqrt[4]{\sqrt[3]{2^{2}}} = \sqrt[4]{(2^{2})^{\frac{1}{3}}}$.Using the power of a power rule $(a^{m})^{n} = a^{m 	imes n}$,we get $(2^{2})^{\frac{1}{3}} = 2^{\frac{2}{3}}$.Now,apply the outer radical: $(2^{\frac{2}{3}})^{\frac{1}{4}} = 2^{\frac{2}{3} 	imes \frac{1}{4}}$.Simplifying the exponent: $\frac{2}{3} 	imes \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$.Thus,the expression simplifies to $2^{\frac{1}{6}}$.Hence,$(B)$ is the correct answer.

$\sqrt[4]{\sqrt[3]{2^{2}}}$ equals

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