443,413 views
30 votes
30 votes
Select the expression that simplifies to 1 / x^1/8

Select the expression that simplifies to 1 / x^1/8-example-1
User Jeru Luke
by
3.1k points

1 Answer

15 votes
15 votes

Answer:


\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)}

User Vytalyi
by
3.3k points