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4: Simplifying Expressions

Last updated

Dec 17, 2024
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- 3.6: Common Volumes
- 4.1: Algebraic Expressions - An Introduction and Using in Applications

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4.1: Algebraic Expressions - An Introduction and Using in Applications
4.2: Laws of Exponents
- 4.2E: Exercises
4.3: Multiplying and Distributing Polynomial Expressions
4.4: Simplifying Ratios of Polynomials
4.5: Dividing Polynomials - Long Division
- 4.5E: Exercises
4.6: Dividing Polynomials - Synthetic Division
4.7: Multiplying and Dividing Rational Expressions
- 4.7E: Exercises
4.8: Adding and Subtracting Rational Expressions
- 4.8E: Exercises
4.9: Simplifying Compound Rational Expressions
- 4.9E: Exercises
4.10: Properties of Radicals and Simplifying Expressions Involving Roots
- 4.10E: Exercises
4.11: Simplifying Radical Expressions
We will simplify radical expressions in a way similar to how we simplified fractions. A fraction is simplified if there are no common factors in the numerator and denominator. To simplify a fraction, we look for any common factors in the numerator and denominator. A radical expression, ⁿ√ a , is considered simplified if it has no factors of mⁿ. So, to simplify a radical expression, we look for any factors in the radicand that are powers of the index.
- 4.11E: Exercises
4.12: Rationalizing Denominators and Numerators
4.13: Simplifying Expressions Involving Positive Rational Exponents
Rational exponents are another way of writing expressions with radicals. When we use rational exponents, we can apply the properties of exponents to simplify expressions.
- 4.13E: Exercises
4.14: Simplifying Expressions Involving Negative Rational Exponents
4.15: Adding, Subtracting, and Multiplying Radical Expressions
Adding radical expressions with the same index and the same radicand is just like adding like terms. We call radicals with the same index and the same radicand like radicals to remind us they work the same as like terms.
- 4.15E: Exercises
4.16: Dividing Radical Expressions
We have used the Quotient Property of Radical Expressions to simplify roots of fractions. We will need to use this property ‘in reverse’ to simplify a fraction with radicals. We give the Quotient Property of Radical Expressions again for easy reference. Remember, we assume all variables are greater than or equal to zero so that no absolute value bars re needed.
- 4.16E: Exercises

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