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

Question

05-05-2022
Mathematics

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

Sagot :

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loneguy loneguy · Answer 1 · 2022-05-05T20:27:50-04:00

Answer:

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

Step-by-step explanation:

[tex]\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}}[/tex]

Sagot :

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