The given expression written in the simplest rational exponent form is [tex]x^{\frac{3}{4} }[/tex]
From the question, we are to write the given expression in exponent form
The given expression is
[tex]\sqrt{x} \times \sqrt[4]{x}[/tex]
In exponent form,
[tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]
and
[tex]\sqrt[4]{x} = x^{\frac{1}{4} }[/tex]
Thus, [tex]\sqrt{x} \times \sqrt[4]{x}[/tex] becomes
[tex]x^{\frac{1}{2} } \times x^{\frac{1}{4} }[/tex]
Applying the multiplication law of indices, we get
[tex]x^{\frac{1}{2} + \frac{1}{4} }[/tex]
= [tex]x^{\frac{3}{4} }[/tex]
Hence, the given expression written in the simplest rational exponent form is [tex]x^{\frac{3}{4} }[/tex]
Learn more on Writing an expression in exponent form here: https://brainly.com/question/4421494
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