Answer :
The choices equivalent to the given expression are options A) (x[tex](x^5)^1^/^4[/tex], C) [tex](\sqrt[4]{x} )^5[/tex] and F) [tex]\sqrt[4]{x^5}[/tex].
What are Rational Exponents?
Rational exponents are numbers which are written in the form of [tex]x^p^/^q[/tex], where x is the base with positive integer and p/q is the rational exponent and q ≠ 0.
Given is a rational exponent [tex]x^5^/^4[/tex].
We have to find the equivalent expression of this.
We have a rule of exponent that,
[tex]x^m^n = (x^m)^n[/tex] or [tex](x^n)^m[/tex]
So using this,
[tex]x^5^/^4[/tex] = [tex](x)^5^*^\frac{1}{4}[/tex] = [tex](x^5)^1^/^4[/tex], which is A.
Now,
[tex](x)^\frac{1}{n}[/tex] = [tex]\sqrt[n]{x}[/tex]
[tex](x^5)^1^/^4[/tex] = [tex]\sqrt[4]{x^5}[/tex], which is F.
Also,
[tex]x^5^/^4[/tex] = [tex](x)^5^*^\frac{1}{4}[/tex] = [tex](x^1^/^4)^5[/tex] = [tex](\sqrt[4]{x} )^5[/tex], which is C.
Hence the correct options are A, C and F.
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