Answer:
[tex](\sqrt[3]{8})^{\frac{1}{4}x}=\sqrt[12]{8}^{x}[/tex]
Step-by-step explanation:
Given : Expression [tex](\sqrt[3]{8})^{\frac{1}{4}x}[/tex]
To find : What is equivalent to given expression ?
Solution :
We can write or solve the given expression as :
[tex](\sqrt[3]{8})^{\frac{1}{4}x}[/tex]
Using exponent rule : [tex]\sqrt[n]{x^m}=(x^m)^\frac{1}{n}=x^\frac{m}{n}[/tex]
[tex]=\sqrt{8^\frac{1}{3}}^{\frac{1}{4}x}[/tex]
[tex]=\sqrt{8}^{\frac{1}{3}\times \frac{1}{4}x}[/tex]
[tex]=\sqrt{8}^{\frac{1}{12}x}[/tex]
or [tex]=\sqrt[12]{8}^{x}[/tex]
or [tex]=\sqrt{2^3}^{\frac{1}{12}x}[/tex]
[tex]=\sqrt{2}^{\frac{1}{4}x}[/tex]
[tex]=\sqrt[4]{2}^{x}[/tex]
These are the possible value equivalent to given expression.
