Answer:
The rational exponent form of given expression is [tex]x^{\frac{5}{2}}[/tex].
Step-by-step explanation:
A number is called a rational number if it can be defined as p/q, where p and q are real numbers and q≠0.
The given expression is
[tex](\sqrt{x})^5[/tex]
It can be written as
[tex](\sqrt{x})^5=(x^{\frac{1}{2}})^5[/tex] [tex][\because \sqrt{x}=(x)^{\frac{1}{2}}][/tex]
Using the power property of exponent we get
[tex](\sqrt{x})^5=x^{\frac{5}{2}}[/tex] [tex][\because (x^m)^n=x^{mn}][/tex]
Here [tex]\frac{5}{2}[/tex] is a rational number.
Therefore the rational exponent form of given expression is [tex]x^{\frac{5}{2}}[/tex].
