Multiplying and Dividing Monomials Solutions Page 27

To simplify expressions involving powers and constants, focus on the exponents. When multiplying, add the exponents of like bases. For example, x² * x³ = x⁵. In cases of division, subtract the exponents of like bases. Thus, x⁵ / x² = x³.

Ensure you are working with similar bases before performing these operations. This principle holds true whether the terms are variables or numbers. For instance, multiplying 3x³ * 2x² results in 6x⁵, since the constants are multiplied and the exponents are added.

When performing division, the same rule applies. In 8x⁶ / 2x³, you divide the constants and subtract the exponents, resulting in 4x³.

As you work through these exercises, be mindful of negative exponents or terms that don’t share common bases. Handling negative exponents involves converting them to the denominator of a fraction. Practice these rules to improve your confidence and speed in simplifying algebraic expressions.