Answer:
Option C, D, E are the correct options.
Step-by-step explanation:
The given expression is [tex]x^{\frac{8}{5}}[/tex]
Now we will check for each option given
A. [tex](x^{5})^{\frac{1}{8}}=x^{\frac{5}{8}}[/tex]
Wrong option.
B.[tex]\sqrt[8]{x^{5}}=x^{\frac{5}{8}}[/tex]
Wrong option
C.[tex](\sqrt[5]{x})^{8}=x^{\frac{8}{5}}[/tex]
Correct option
D.[tex]\sqrt[5]{x^{8}}=x^{\frac{8}{5}}[/tex]
Correct option
E.[tex](x^{8})^{\frac{1}{5}}=x^{\frac{8}{5}}[/tex]
Correct option
F.[tex](\sqrt[8]{x})^{5}=x^{\frac{5}{8}}[/tex]
Wrong option
Answer :
C , D, E are equivalent to [tex]x^{\frac{8}{5} }[/tex].
Step by step explanation :
Given: [tex]x^{\frac{8}{5} }[/tex].
To find : Which of the following choices are equivalent to the expression below .
Solution : We have given that [tex]x^{\frac{5}{8} }[/tex].
Now , we will check all option .
By exponent rule : [tex](a^{b} )^c= a^{bc}[/tex]
A . [tex](x^{5} )^\frac{1}{8}[/tex] = [tex]x^{\frac{5}{8} }[/tex].
Wrong
B .[tex]\sqrt[8]{x^{5} }[/tex] = [tex]x^{\frac{5}{8} }[/tex].
Wrong
C. [tex](\sqrt[5]{x} )^8[/tex] = [tex]x^{\frac{8}{5} }[/tex].
Correct
D. [tex]\sqrt[5]{x^{8} }[/tex] =[tex]x^{\frac{8}{5} }[/tex].
Correct
E. [tex](x^{8} )^\frac{1}{5}[/tex] = [tex]x^{\frac{8}{5} }[/tex].
Correct
F. [tex](\sqrt[8]{x} )^5[/tex] = [tex]x^{\frac{5}{8} }[/tex].
Wrong .
Therefore, C , D, E are equivalent to [tex]x^{\frac{8}{5} }[/tex].
