Precalculus 1.2.5p1 - Practice with Rational Exponents

Practice Problems: Simplifying Rational Exponents Test your understanding of rational exponents with eight challenging expressions! In this video, we walk through step-by-step solutions—combining exponents, distributing powers, and checking domain restrictions. Pause the video to try each problem on your own, then follow along as we simplify: Adding and subtracting fractional exponents on a common base Distributing a fractional exponent over products and quotients Converting between radical notation and rational exponents Identifying when variable restrictions (like non-negativity) apply Whether you’re reinforcing your algebra skills or prepping for exams, these practice problems will solidify your comfort with fractional powers. --- Problems Covered 1. Multiply and add exponents: a^(2/5) × a^(7/5) 2. Multiply and divide exponents: (a^(2/7) × a^(11/7)) / a^(1/7) 3. Distribute a 3/2 power over 8a^5b^6 4. Combine nested radicals as rational exponents 5. Distribute a 5th power and simplify mixed exponents 6. Translate radicals to exponents: sqrt(4x) × cube_root(x^2) 7. Simplify cube_root(x^2) expressions with like terms 8. Tackle complex radical products in exponent form Key Concepts Exponent addition/subtraction Power of a product/quotient Root to rational exponent conversion Domain restrictions for even roots --- #RationalExponents #AlgebraPractice #MathWorkout #FractionalPowers #RadicalRules #ExponentLaws #MathStudy #Precalculus #STEMLearning #MathHelp