Question

4 square root (1/x) power -12 whole power -2/3​

Answer 1

$\textbf{Given:}$

$\mathsf{\left[\sqrt[4]{\left(\dfrac{1}{x}\right)^{-12}}\right]^\frac{-2}{3}}$

$\textbf{To simplify:}$

$\mathsf{\left[\sqrt[4]{\left(\dfrac{1}{x}\right)^{-12}}\right]^\frac{-2}{3}}$

$\textbf{Solution:}$

$\textbf{Formula used:}$

$\boxed{\mathsf{(a^m)^n=a^{mn}}}$

$\textsf{Consider,}$

$\mathsf{\left[\sqrt[4]{\left(\dfrac{1}{x}\right)^{-12}}\right]^\frac{-2}{3}}$

$\mathsf{=\left[\left(\left(\dfrac{1}{x}\right)^{-12}\right)^\frac{1}{4}}\right]^\frac{-2}{3}}$

$\mathsf{=\left[\left(\dfrac{1}{x}\right)^{-3}\right]^\frac{-2}{3}}$

$\mathsf{=\left[(x^{-1})^{-3}\right]^\frac{-2}{3}}$

$\mathsf{=\left[x^3\right]^\frac{-2}{3}}$

$\mathsf{=x^{-2}}$

$\mathsf{=\dfrac{1}{x^2}}$

$\implies\boxed{\mathsf{\left[\sqrt[4]{\left(\dfrac{1}{x}\right)^{-12}}\right]^\frac{-2}{3}=\dfrac{1}{x^2}}}$

Answer 2

Answer:

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