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Mastering Algebra II: Simplifying nth Roots & Rational Exponents

Learn to evaluate nth roots, use rational exponents, and simplify expressions. Find real nth roots without a calculator. Examples included for practice. Understand rational exponents and rewrite expressions accordingly. Enhance your algebra skills today!

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Mastering Algebra II: Simplifying nth Roots & Rational Exponents

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  1. Algebra II 6.1: Evaluate nth Roots and Use Rational Exponents

  2. Simplify the expression.

  3. Simplify the expression.

  4. Simplify the expression.

  5. Simplify the expression.

  6. Finding real nth roots of a. • If bn = a, then b is an nth root of a. • Don’t forget about for even roots. • 22 = 4 and (-2)2 = 4, therefore the 2nd root of 4 would be 2.

  7. Examples: Find the indicated realnth root(s) of a without using a calculator. 1.) n = 3, a = -64 2.) n = 3, a = 216

  8. Examples: Find the indicated realnth root(s) of a without using a calculator. 3.) n = 4, a = -16 4.) n = 4, a = 81

  9. Examples: Find the indicated realnth root(s) of a without using a calculator. 5.) n = 5, a = 0 6.) n = 5, a = 243

  10. Rational Exponents – Key Concept

  11. Rewrite the expression using rational exponent notation.

  12. Rewrite the expression using radical notation.

  13. Evaluate the expression without using a calculator.

  14. Evaluate the expression without using a calculator.

  15. Evaluate the expression using a calculator. Round to the nearest hundredth.

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