The value of left{left(sqrt[n]{x^{2}}right)^{ | vedclass

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Question

(A) Given expression: $\left\{\left(\sqrt[n]{x^{2}}\right)^{n / 2}\right\}^{2}$Step $1$: Simplify the inner term $\sqrt[n]{x^{2}}$. This can be writte

Vedclass · Accepted Answer

$x^{2}$

Vedclass · Answer

(A) Given expression: $\left\{\left(\sqrt[n]{x^{2}}\right)^{n / 2}\right\}^{2}$Step $1$: Simplify the inner term $\sqrt[n]{x^{2}}$. This can be written as $(x^{2})^{1/n} = x^{2/n}$.Step $2$: Substitute this back into the expression: $\left\{(x^{2/n})^{n/2}\right\}^{2}$.Step $3$: Use the power rule $(a^{m})^{n} = a^{m \cdot n}$. The expression becomes $\left\{x^{(2/n) \cdot (n/2)}\right\}^{2}$.Step $4$: Simplify the exponent: $(2/n) \cdot (n/2) = 1$. So,the expression simplifies to $\{x^{1}\}^{2}$.Step $5$: Finally,$x^{1 \cdot 2} = x^{2}$.

The value of $\left\{\left(\sqrt[n]{x^{2}}\right)^{n / 2}\right\}^{2}$ is

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