To simplify the fraction \(\frac{15a^2b^3}{5a^3b}\):

1. Divide the coefficients: \(\frac{15}{5} = 3\).
2. Apply the rule of exponents for the \(a\) terms: \(\frac{a^2}{a^3} = a^{2-3} = a^{-1} = \frac{1}{a}\).
3. Apply the rule of exponents for the \(b\) terms: \(\frac{b^3}{b} = b^{3-1} = b^2\).

Now, the simplified expression is:

\[
\frac{15a^2b^3}{5a^3b} = \frac{3b^2}{a}
\]

Would you like further explanation or more details?

Here are 5 related questions:
1. How do you simplify a fraction with different powers of variables?
2. What are the rules for handling negative exponents?
3. How would this expression change if the powers of \(a\) and \(b\) were higher?
4. Can this expression be factored further under certain conditions?
5. How do coefficients affect the simplification process of a fraction?

**Tip:** Always subtract exponents when dividing like bases.

Learn how to simplify the fraction 15a^2b^3/5a^3b by applying the rules of exponents and dividing coefficients. This step-by-step guide walks through the simplification process for algebraic fractions, ideal for students in Grades 8-10.

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