Which of the following choices are equivalent to the expression below? Check all that apply. HELP PLEASE PLEASE HELP PLEASE PLEASE PLEASE
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The choices which are equivalent to the given expression is:
[tex]A.\ \ (x^5)^{\frac{1}{4}}[/tex]
[tex]C.\ \ (\sqrt[4]{x})^5[/tex]
[tex]F.\ \ \sqrt[4]{x^5}[/tex]
We are given a expression in terms of the variable x as:
[tex]x^{\frac{5}{4}}[/tex]
Now, we know that any general expression of the form:
[tex]x^{\frac{m}{n}}[/tex] could also be represented by:
[tex](x^m)^{\frac{1}{n}}[/tex] or [tex](x^{\frac{1}{n}})^m[/tex] or [tex]\sqrt[n]{x^m}[/tex] or [tex](\sqrt[n]{x})^m[/tex]
Here in this expression we have:
[tex]m=5\ and\ n=4[/tex]
Hence, the equivalent expressions are:
Option: A , Option: C and Option: F