To simplify the expression [tex]\(\frac{2 m^2 n^3 p}{4 m n p}\)[/tex], we need to perform the following steps:
1. Factorize constants and like terms:
The numerator of the fraction is [tex]\(2 m^2 n^3 p\)[/tex], and the denominator is [tex]\(4 m n p\)[/tex].
2. Simplify the constants:
The fraction has constants 2 and 4, so simplify [tex]\( \frac{2}{4} \)[/tex]:
[tex]\[
\frac{2}{4} = \frac{1}{2}
\][/tex]
3. Cancel out common variables:
We have [tex]\(m^2\)[/tex] in the numerator and [tex]\(m\)[/tex] in the denominator. We can cancel out one [tex]\(m\)[/tex] from both:
[tex]\[
m^2 \div m = m
\][/tex]
Similarly, we have [tex]\(n^3\)[/tex] in the numerator and [tex]\(n\)[/tex] in the denominator. We can cancel out one [tex]\(n\)[/tex] from both:
[tex]\[
n^3 \div n = n^2
\][/tex]
Finally, we have [tex]\(p\)[/tex] in both the numerator and the denominator. We can cancel [tex]\(p\)[/tex] from both sides:
[tex]\[
p \div p = 1
\][/tex]
4. Combine the simplified terms:
After simplifying and canceling common terms, the remaining expression is:
[tex]\[
\frac{m^2 n^3}{4 m n} = \frac{m \cdot n^2}{2}
\][/tex]
So the simplified form of the expression [tex]\(\frac{2 m^2 n^3 p}{4 m n p}\)[/tex] is:
[tex]\[
\boxed{\frac{m n^2}{2}}
\][/tex]
