Question

Select the expression that simplifies to 1 / x^1/8

Answer 1

Answer:

$\left(\displaystyle \sqrt[3]{x^{-\tfrac 35}}\right)^{\tfrac 58}$

Step-by-step explanation:

$\left(\displaystyle \sqrt[3]{x^{-\tfrac 35}}\right)^{\tfrac 58}\\\\\\=\left[ \left(\displaystyle x^{-\tfrac 35} \right)^{\tfrac 13 \right]^{\tfrac 58}\\\\\\=\left( \displaystyle x^{-\tfrac 35}\right)^{\tfrac 5{24}}\\\\\\=x^{ \displaystyle -\tfrac{3}{24} \right}\\\\\\=x^{\displaystyle -\tfrac 18 }\\\\\\=\dfrac 1{x^{\tfrac 18}}$