Question

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

Answer 1

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

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 )\\\\\\=\frac 1{x^(\tfrac 18)}`