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

Verified step by step guidance

1. Identify the operation to be performed: multiplication of two fractions \( \frac{2x}{5} \) and \( \frac{10}{x^2} \).
2. Multiply the numerators together: \( 2x \times 10 \).
3. Multiply the denominators together: \( 5 \times x^2 \).
4. Simplify the resulting fraction by canceling out any common factors in the numerator and the denominator.
5. Write the simplified fraction in its lowest terms.

Key Concepts

Multiplication of Fractions

To multiply fractions, you multiply the numerators together and the denominators together. For example, in the expression (a/b) * (c/d), the result is (a*c)/(b*d). This concept is essential for simplifying expressions involving fractions, as it allows for straightforward calculations.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). This process makes fractions easier to work with and understand, ensuring that the final answer is presented in the simplest form.

Variable Exponents

In algebra, variables can have exponents that indicate how many times the variable is multiplied by itself. When multiplying variables with exponents, you add the exponents if the bases are the same. Understanding how to manipulate these exponents is crucial for simplifying expressions that involve variables.