Sure, let's break down the solution for the expression [tex]\(\frac{7 x^4}{\sqrt{2 x-8}}\)[/tex] step-by-step.
1. Expression Setup:
We are given the mathematical expression:
[tex]\[
\frac{7 x^4}{\sqrt{2 x-8}}
\][/tex]
2. Numerator:
The numerator of the expression is [tex]\(7 x^4\)[/tex].
3. Denominator:
The denominator of the expression is [tex]\(\sqrt{2 x-8}\)[/tex].
4. Simplifying the Denominator:
The term inside the square root is [tex]\(2 x - 8\)[/tex]. So the expression under the square root remains [tex]\(2 x - 8\)[/tex].
5. Combining the Parts:
Putting everything together, the expression remains:
[tex]\[
\frac{7 x^4}{\sqrt{2 x - 8}}
\][/tex]
Therefore, the expression in its simplest form is:
[tex]\[
\frac{7 x^4}{\sqrt{2 x - 8}}
\][/tex]
