Sure, let's simplify the given expression step-by-step:
The given expression is:
[tex]\[
\frac{2 x^3 + 8 x^3}{(5 x)(2 x^2)}
\][/tex]
Step 1: Simplify the numerator
The numerator is [tex]\(2 x^3 + 8 x^3\)[/tex]. We can combine like terms:
[tex]\[
2 x^3 + 8 x^3 = (2 + 8) x^3 = 10 x^3
\][/tex]
So, the numerator becomes [tex]\(10 x^3\)[/tex].
Step 2: Simplify the denominator
The denominator is [tex]\((5 x)(2 x^2)\)[/tex]. We can multiply these terms:
[tex]\[
(5 x)(2 x^2) = 5 \cdot 2 \cdot x \cdot x^2 = 10 x^3
\][/tex]
So, the denominator becomes [tex]\(10 x^3\)[/tex].
Step 3: Put the simplified numerator and denominator into the fraction
Now, we substitute back the simplified numerator and denominator into the fraction:
[tex]\[
\frac{10 x^3}{10 x^3}
\][/tex]
Step 4: Simplify the fraction
Since the numerator and the denominator are the same, they cancel each other out:
[tex]\[
\frac{10 x^3}{10 x^3} = 1
\][/tex]
So, the simplified expression is:
[tex]\[
1
\][/tex]
Therefore, the simplified result of the given expression is [tex]\(1\)[/tex].
