CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms (2x/5) • (10/x²)

Verified step by step guidance

1. Rewrite the given expression clearly: \(\frac{2x}{5} \cdot \frac{10x}{x^{2}}\).
2. Multiply the numerators together and the denominators together: \(\frac{2x \times 10x}{5 \times x^{2}}\).
3. Simplify the numerator by multiplying the coefficients and variables: \(2 \times 10 = 20\) and \(x \times x = x^{2}\), so numerator becomes \$20x^{2}$.
4. Simplify the denominator: \(5 \times x^{2} = 5x^{2}\).
5. Write the fraction as \(\frac{20x^{2}}{5x^{2}}\) and then simplify by canceling common factors in numerator and denominator.

Key Concepts

Multiplication of Rational Expressions

Multiplying rational expressions involves multiplying the numerators together and the denominators together. Each expression is treated like a fraction, and the product is simplified by combining terms appropriately.

Simplifying Algebraic Expressions

Simplifying algebraic expressions requires factoring polynomials and canceling common factors in the numerator and denominator. This process reduces the expression to its lowest terms, making it easier to interpret and use.

Laws of Exponents

When multiplying expressions with variables raised to powers, apply the laws of exponents by adding the exponents of like bases. This is essential for correctly simplifying terms such as x and x² in the given problem.