Respuesta :

kudzordzifrancis

Answer:

See explanations

Step-by-step explanation:

We want to  find the expression that is equivalent to

[tex](\sqrt[3]{8})^{\frac{1}{4}x }[/tex]

Recall that: [tex]2\times 2\times 2=2^3=8[/tex], [tex]\implies \sqrt[3]{8}=2[/tex]

We apply this knowledge to obtain:

[tex](\sqrt[3]{8})^{\frac{1}{4}x}=(2)^{\frac{1}{4}x }[/tex]

[tex](\sqrt[3]{8})^{\frac{1}{4}x}=(2^\frac{1}{4})^x[/tex]

Recall again that:

[tex]a^{\frac{1}{n} }=\sqrt[n]{a}[/tex]

[tex](\sqrt[3]{8})^{\frac{1}{4}x}=(\sqrt[4]{2})^x }[/tex]

The answer could be in varying forms.

Unfortunately, you have not provided the options

We need the options so that we can give you the correct choice.

The expression that is equivalent to the given expression [tex](\sqrt[3]{8})^{\frac{1}{4}x}[/tex] is [tex](\sqrt[4]{2})^{x}[/tex] and this can be determined by using the arithmetic operations.

Given :

Expression - [tex](\sqrt[3]{8})^{\frac{1}{4}x}[/tex]

To evaluate the given expression following steps can be used:

Step 1 - Write the given expression.

[tex]=(\sqrt[3]{8})^{\frac{1}{4}x}[/tex]

Step 2 - Write 8 as [tex]2^3[/tex] in the above expression.

[tex]=(\sqrt[3]{2^3})^{\frac{1}{4}x}[/tex]

Step 3 - [tex]\sqrt[3] {2^3 }[/tex]  becomes 2 in the above expression.

[tex]=(2)^{\frac{1}{4}x}[/tex]

Step 4 - Rewrite the above expression.

[tex]=(\sqrt[4]{2})^{x}[/tex]

For more information, refer to the link given below:

https://brainly.com/question/17921485

Otras preguntas