Multiply or divide, as indicated. See Example 3. (15p³ / 9p²) • (12p / 10p³)

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Rewrite the expression clearly as a multiplication of two fractions: \(\frac{15p^{3}}{9p^{2}} \times \frac{12p}{10p^{3}}\).

Simplify each fraction separately by dividing the coefficients (numerical parts) and applying the laws of exponents to the variable parts. Recall that \(\frac{p^{a}}{p^{b}} = p^{a-b}\).

For the first fraction, simplify \(\frac{15}{9}\) by dividing numerator and denominator by their greatest common divisor, and simplify \(\frac{p^{3}}{p^{2}}\) by subtracting exponents.

For the second fraction, simplify \(\frac{12}{10}\) similarly, and simplify \(\frac{p}{p^{3}}\) by subtracting exponents.

After simplifying both fractions, multiply the simplified coefficients and multiply the powers of \(p\) by adding their exponents according to the multiplication rule \(p^{m} \times p^{n} = p^{m+n}\).

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