To solve the given expression [tex]\(\frac{2 x^3}{y} \times \frac{4 y}{x^2}\)[/tex], follow these steps:
1. Write down the expression:
[tex]\[
\frac{2 x^3}{y} \times \frac{4 y}{x^2}
\][/tex]
2. Multiply the numerators together:
- The numerators are [tex]\(2 x^3\)[/tex] and [tex]\(4 y\)[/tex].
[tex]\[
2 x^3 \times 4 y = 8 x^3 y
\][/tex]
3. Multiply the denominators together:
- The denominators are [tex]\(y\)[/tex] and [tex]\(x^2\)[/tex].
[tex]\[
y \times x^2 = x^2 y
\][/tex]
4. Combine these results into a single fraction:
[tex]\[
\frac{8 x^3 y}{x^2 y}
\][/tex]
5. Simplify the fraction:
- Here you can cancel out like terms in the numerator and the denominator.
- The [tex]\(y\)[/tex] terms cancel each other out.
- You are left with [tex]\(\frac{8 x^3}{x^2}\)[/tex].
6. Further simplify the remaining expression:
- Simplify the [tex]\(x\)[/tex] terms: [tex]\(\frac{x^3}{x^2} = x\)[/tex].
[tex]\[
\frac{8 x^3}{x^2} = 8 x
\][/tex]
So, after simplifying the original expression, the final result is:
[tex]\[
8x
\][/tex]
