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

Verified step by step guidance

1. Step 1: Simplify each fraction separately. Start with the first fraction $\frac{15p^3}{9p^2}$.
2. Step 2: Simplify $\frac{15p^3}{9p^2}$ by dividing the coefficients and subtracting the exponents of $p$.
3. Step 3: Simplify the second fraction $\frac{12p}{10p^3}$ by dividing the coefficients and subtracting the exponents of $p$.
4. Step 4: Multiply the simplified results of the two fractions together.
5. Step 5: Simplify the resulting expression by combining like terms and reducing any common factors.

Key Concepts

Multiplication of Fractions

To multiply fractions, you multiply the numerators together and the denominators together. For example, if you have two fractions a/b and c/d, the product is (a*c)/(b*d). This principle is essential for simplifying expressions involving variables and coefficients.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves reducing them to their simplest form by combining like terms and canceling common factors. This process is crucial when working with fractions that contain variables, as it helps to make calculations more manageable and clearer.

Properties of Exponents

The properties of exponents govern how to handle expressions involving powers of variables. Key rules include the product of powers (a^m * a^n = a^(m+n)) and the quotient of powers (a^m / a^n = a^(m-n)). Understanding these rules is vital for manipulating expressions with variables raised to powers.