Question

Rewrite in simplest rational exponent form exFormula1" title="\sqrt{x} * \sqrt[4]{x}" alt="\sqrt{x} * \sqrt[4]{x}" align="absmiddle" class="latex-formula"> Show each step of your process.

Answer 1

The given expression written in the simplest rational exponent form is $x^{\frac{3}{4} }$

Writing an Expression in Exponent form

From the question, we are to write the given expression in exponent form

The given expression is

$\sqrt{x} \times \sqrt[4]{x}$

In exponent form,

$\sqrt{x} = x^{\frac{1}{2} }$

and

$\sqrt[4]{x} = x^{\frac{1}{4} }$

Thus,  $\sqrt{x} \times \sqrt[4]{x}$ becomes

$x^{\frac{1}{2} } \times x^{\frac{1}{4} }$

Applying the multiplication law of indices, we get

$x^{\frac{1}{2} + \frac{1}{4} }$

= $x^{\frac{3}{4} }$

Hence, the given expression written in the simplest rational exponent form is $x^{\frac{3}{4} }$

Learn more on Writing an expression in exponent form here: brainly.com/question/4421494

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