Algebra 2 · Grades 9 to 11
Rational exponents and radicals
Powers written as roots, and equations with square roots.
The idea
A rational exponent joins a power and a root. The fraction 3/4 in x^(3/4) means the fourth root, then the third power.
A radical equation has the variable inside a square root. Square both sides to remove the root, then solve and check.
Worked examples
- How to Simplify Rational Exponents Simplify 16^(3/4) by taking the root first. Three steps, the reason for the order, and the exponent mistakes to avoid.
- How to Solve a Radical Equation Solve sqrt(x + 5) = 4 by squaring both sides. Four steps, the check, and the false-solution mistake to avoid.
- How to Solve a Quadratic Equation by Factoring Solve x^2 - 5x + 6 = 0 by factoring. Four steps, the zero-product reason, and the factoring mistakes that lose solutions.
Practice this topic
3 problems with answers.