Sure, let's work through the conversion of the expression [tex]\(6 x^{\frac{3}{4}}\)[/tex] into radical form step-by-step.
Given expression: [tex]\(6 x^{\frac{3}{4}}\)[/tex]
To convert this expression into radical form, we need to use the rule for converting exponents to radicals. The general rule states that:
[tex]\[ x^{\frac{n}{d}} = \sqrt[d]{x^n} \][/tex]
In our case, we have [tex]\(x^{\frac{3}{4}}\)[/tex]. This means [tex]\(x\)[/tex] is raised to the power of [tex]\(\frac{3}{4}\)[/tex]. According to the rule:
[tex]\[ x^{\frac{3}{4}} = \sqrt[4]{x^3} \][/tex]
So, we can write the given expression [tex]\(6 x^{\frac{3}{4}}\)[/tex] as:
[tex]\[ 6 x^{\frac{3}{4}} = 6 \sqrt[4]{x^3} \][/tex]
Therefore, the correct representation of [tex]\(6 x^{\frac{3}{4}}\)[/tex] in radical form is:
[tex]\[ \boxed{6 \sqrt[4]{x^3}} \][/tex]
