Perform the indicated operation, and write each answer in lowest terms. 2x/5 ∙ 10/x²

Verified step by step guidance

1. Identify the given expression to multiply: \(\frac{2x}{5} \times \frac{10}{x^{2}}\).
2. Multiply the numerators together and the denominators together: \(\frac{2x \times 10}{5 \times x^{2}}\).
3. Simplify the numerator and denominator separately: numerator becomes \$20x\(, denominator becomes \)5x^{2}$, so the expression is \(\frac{20x}{5x^{2}}\).
4. Factor and reduce common factors in numerator and denominator: divide both numerator and denominator by \$5x$ to simplify the fraction.
5. Write the simplified expression after canceling common factors, ensuring the answer is in lowest terms.

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, so the product is a new fraction formed by these products.

Simplifying Algebraic Expressions

Simplifying involves reducing expressions to their simplest form by canceling common factors in the numerator and denominator. This often requires factoring and recognizing common terms to eliminate.

Exponents and Their Properties

Understanding how to handle exponents is crucial, especially when multiplying terms with the same base. The product rule states that when multiplying like bases, you add their exponents, which helps simplify expressions involving powers.