Final answer:
To multiply rational algebraic expressions, multiply the numerators and denominators separately, simplify by cancelling common factors, combine like terms, apply the rules for exponents, and check that the final expression is reasonable.
Step-by-step explanation:
To multiply rational algebraic expressions, one should follow these steps:
- Write out the rational expressions that you want to multiply.
- Multiply the numerators (the top numbers) together.
- Multiply the denominators (the bottom numbers) together.
- Simplify the algebra by cancelling out any common factors between the numerator and the denominator.
- Eliminate terms wherever possible to further simplify the expression.
- When dealing with exponents, multiply the coefficients (digit terms) and add the exponents for like bases.
- Ensure your final expression makes sense and the units (if any) cancel out correctly.
- Check the final simplified expression to see if it is reasonable and correctly simplified.
Remember that simplifying the rational expression by eliminating terms and combining like terms wherever possible is a key step in the multiplication process.
In the case of exponents, applying the rule of adding exponents when multiplying exponential terms ensures the correct algebraic manipulation.