Question

Which of the following choices are equivalent to the expression below ?

Answer 1

Answer:

Option C, D, E are the correct options.

Step-by-step explanation:

The given expression is $x^{\frac{8}{5}}$

Now we will check for each option given

A. $(x^{5})^{\frac{1}{8}}=x^{\frac{5}{8}}$

Wrong option.

B.$\sqrt[8]{x^{5}}=x^{\frac{5}{8}}$

Wrong option

C.$(\sqrt[5]{x})^{8}=x^{\frac{8}{5}}$

Correct option

D.$\sqrt[5]{x^{8}}=x^{\frac{8}{5}}$

Correct option

E.$(x^{8})^{\frac{1}{5}}=x^{\frac{8}{5}}$

Correct option

F.$(\sqrt[8]{x})^{5}=x^{\frac{5}{8}}$

Wrong option

Answer 2

Answer :

C , D, E are equivalent to  $x^{\frac{8}{5} }$.

Step by step explanation :

Given: $x^{\frac{8}{5} }$.

To find :  Which of the following choices are equivalent to the expression below .

Solution : We have given that  $x^{\frac{5}{8} }$.

Now , we will check all option .

By exponent rule : $(a^{b} )^c= a^{bc}$

A . $(x^{5} )^\frac{1}{8}$ =  $x^{\frac{5}{8} }$.

Wrong

B .$\sqrt[8]{x^{5} }$ =  $x^{\frac{5}{8} }$.

Wrong

C. $(\sqrt[5]{x} )^8$ =  $x^{\frac{8}{5} }$.

Correct

D. $\sqrt[5]{x^{8} }$ =$x^{\frac{8}{5} }$.

Correct

E.  $(x^{8} )^\frac{1}{5}$ = $x^{\frac{8}{5} }$.

Correct

F. $(\sqrt[8]{x} )^5$ = $x^{\frac{5}{8} }$.

Wrong .

Therefore, C , D, E are equivalent to  $x^{\frac{8}{5} }$.