Final answer:
To multiply rational expressions, multiply the numerators together and the denominators together, simplifying as needed. If an expression can't be simplified directly, perform the multiplication and rearrange to simplify.
Step-by-step explanation:
Multiplying Rational Expressions
To multiply rational expressions, we follow a similar process as multiplying fractions. The rule for multiplying two fractions is to multiply the numerators (top numbers) together and multiply the denominators (bottom numbers) together. For example, ¾ × ⅓ equals 3 × 2 over 4 × 5, which simplifies to 6 over 20 and then further simplifies to 3 over 10 after dividing both the numerator and denominator by their greatest common factor.
Multiplication of Exponentials
When dealing with exponential terms, the multiplication of exponentials involves multiplying the digit terms (coefficients) as usual, while the exponents of the exponential terms are added together. For instance, x^2 × x^3 becomes x^(2+3), which simplifies to x^5.
In cases where the expression cannot be simplified directly, the full multiplication must be carried out and then possibly rearranged to combine like terms or to cancel out factors across the numerator and the denominator. As a reminder, when multiplying exponents with the same base, we add the exponents.
If we consider division, the process is similar in that we would divide the coefficients and subtract the exponents of the exponential terms. However, this is not typically relevant when just multiplying expressions.