To simplify the expression \( 5m^2n^3 \times 3mn^4 \):

1. Multiply the numerical coefficients:
   \[
   5 \times 3 = 15
   \]

2. Multiply the powers of \( m \):
   \[
   m^2 \times m = m^{2+1} = m^3
   \]

3. Multiply the powers of \( n \):
   \[
   n^3 \times n^4 = n^{3+4} = n^7
   \]

So, the simplified expression is:
\[
15m^3n^7
\]

Would you like any further details or explanations?

### Related questions:
1. How do you multiply variables with exponents?
2. What is the rule for multiplying powers of the same base?
3. How do you simplify expressions with both variables and coefficients?
4. How does distributing work in more complex expressions?
5. What happens when multiplying terms with different variables?

### Tip:
Always combine like terms (same base and variable) when simplifying expressions with exponents.

This page provides a step-by-step guide to simplifying the algebraic expression 5m^2n^3 x 3mn^4. Learn how to multiply variables with exponents and coefficients, using exponent rules. Suitable for students in Grades 8-10.

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