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The provided question asks to simplify the following expression:

\[
\frac{3m^2n^{-3}}{15n^2m^4}
\]

### Step 1: Simplify the constants
The constants in the expression are 3 and 15. Simplify this as:

\[
\frac{3}{15} = \frac{1}{5}
\]

### Step 2: Simplify the \(m\)-terms
You have \(m^2\) in the numerator and \(m^4\) in the denominator. Using the law of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we subtract the exponents of \(m\):

\[
\frac{m^2}{m^4} = m^{2-4} = m^{-2}
\]

### Step 3: Simplify the \(n\)-terms
You have \(n^{-3}\) in the numerator and \(n^2\) in the denominator. Similarly, subtract the exponents of \(n\):

\[
\frac{n^{-3}}{n^2} = n^{-3-2} = n^{-5}
\]

### Step 4: Combine everything
Now, combining all the simplified terms together:

\[
\frac{3m^2n^{-3}}{15n^2m^4} = \frac{m^{-2}n^{-5}}{5}
\]

Thus, the simplified expression is:

\[
\frac{m^{-2}n^{-5}}{5}
\]

### Step 5: Match with the answer choices
This matches option A:

\[
\boxed{A. \frac{m^{-2}n^{-5}}{5}}
\]

Let me know if you need more details or have any questions. 

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Here are 5 related questions for further practice:

1. Simplify \(\frac{6a^3b^{-2}}{18a^5b}\).
2. Simplify \(\frac{4x^2y^{-4}}{16x^{-3}y^5}\).
3. Find the result of \(\frac{5p^4q^{-1}}{20p^2q^3}\).
4. Simplify \(\frac{7x^{-2}y^3}{14x^5y^{-2}}\).
5. Solve \(\frac{2m^{-1}n^2}{8m^3n^{-1}}\).

### Tip:
When simplifying algebraic fractions, always handle constants separately and apply exponent rules like \(\frac{a^m}{a^n} = a^{m-n}\) for like bases.

Simplify the expression: 3m^2n^-3 / 15n^2m^4.

Learn how to simplify the algebraic expression 3m^2n^-3 / 15n^2m^4 using exponent rules. This problem is suitable for students in Grades 9-11 and covers key concepts like exponent laws and simplifying algebraic fractions.

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