CLEP College Algebra

CLEP College Algebra covers fundamental algebraic concepts and skills necessary for success in college-level mathematics courses.

Advanced Topics

Exponents, Radicals, and Rational Expressions

Working with Exponents

Exponents tell you how many times to multiply a number by itself. The rules of exponents make calculations easier and help simplify expressions.

  • \( a^m \cdot a^n = a^{m+n} \)
  • \( (a^m)^n = a^{mn} \)

Understanding Radicals

Radicals are roots, like square roots (\( \sqrt{x} \)). Simplifying radicals means expressing them in the simplest form.

Rational Expressions

These are fractions with polynomials in the numerator, denominator, or both. You can add, subtract, multiply, and divide them, but always factor and reduce!

Why It Matters

These concepts appear in science (calculating energy), engineering, and finance (interest rates).

Examples

  • Simplify \( (x^2)^3 = x^6 \) using exponent rules.

  • Reduce \( \frac{x^2 - 9}{x + 3} \) to \( x - 3 \) after factoring.

In a Nutshell

Exponents, radicals, and rational expressions extend your algebra skills to work with more complex numbers and relationships.