Multiply or divide, as indicated. 15p³/9p² * 12p/10p³

Verified step by step guidance

1. Start by writing the entire expression as a single fraction multiplication: \(\frac{15p^3}{9p^2} \times \frac{12p}{10p^3}\).
2. Combine the numerators and denominators into one fraction: \(\frac{15p^3 \times 12p}{9p^2 \times 10p^3}\).
3. Multiply the coefficients (numbers) in the numerator and denominator separately: numerator is \(15 \times 12\), denominator is \(9 \times 10\).
4. Apply the laws of exponents to multiply powers of \(p\): when multiplying like bases, add the exponents. So in the numerator, \(p^3 \times p^1 = p^{3+1} = p^4\), and in the denominator, \(p^2 \times p^3 = p^{2+3} = p^5\).
5. Simplify the fraction by reducing the coefficients to lowest terms and subtract the exponents of \(p\) in numerator and denominator (since \(\frac{p^a}{p^b} = p^{a-b}\)).

Key Concepts

Multiplication and Division of Algebraic Fractions

When multiplying or dividing algebraic fractions, multiply or divide the numerators together and the denominators together. Simplify the resulting fraction by factoring and reducing common factors to make the expression simpler.

Laws of Exponents

Exponents indicate repeated multiplication of a base. When multiplying like bases, add their exponents; when dividing, subtract the exponents. For example, p^3 * p^1 = p^(3+1) = p^4, and p^3 / p^2 = p^(3-2) = p^1.

Simplifying Algebraic Expressions

Simplifying involves reducing expressions to their simplest form by canceling common factors, combining like terms, and applying arithmetic operations. This makes expressions easier to interpret and use in further calculations.