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## Powers, Roots and Radicals Review

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**Simplifying Radicals**Explanation Adding and Subtracting Rational Exponents Click on a topic to review, then click practice for some problems! Practice Practice Practice Multiplying Radicals Dividing Radicals Explanation Powers, Roots and Radicals Review Solving Equations Practice Practice Practice**Simplifying Radicals**Example: Simplify • Step 1: Put all numbers in prime factorization form (make a factor tree) • Step 2: Divide each exponent under the radical by the index. This will tell you what can be taken out of the radical and what is left. • Step 3: Simplify if necessary outside the radical and within the radicand. • Don’t forget absolute value if the index is even and a resulting power on the outside of the radical is odd. Show Step 1 Show Step 2 Show Step 3 Practice Home**Simplifying Radicals Practice**Simplify the Expressions Answer Answer Home**Multiplying Radicals Practice**• Step 1: Multiply the numbers/variables on the outside of the radical, and then multiply the numbers/variables on the inside of the radical. • Step 2: Simplify [See Simplifying Radicals for help] Example: Practice Home**Multiplying Radicals Practice**Multiply the Expressions Answer Answer This is an example of multiplying conjugates. Remember, Home**Dividing Radicals**A simplified answer can NEVER have a radical in the denominator. If there is, you must RATIONALIZE the denominator. One term in the denominator: Two terms in the denominator: • Step 1: Simplify all radicals. • Step 2: Multiply both numerator and denominator by the same radical. To find the appropriate radical, subtract the index from each exponent in the radicand of the denominator. • Step 3: Multiply and simplify. • Step 1: Simplify all radicals. • Step 2: Multiply both numerator and denominator by the conjugate of the denominator. • Step 3: Multiply and simplify. Example: Example: Practice Home**Dividing Radicals Practice**Divide the Expressions Answer Answer Multiply by Multiply by Home**Adding and Subtracting Radicals**• Step 1: Simplify all terms. • Step 2: Combine LIKE terms. Like terms have identical indices and radicands.Add or subtract the coefficients in front of the radicals and KEEP THE RADICAL PART THE SAME Example: Practice Home**Adding and Subtracting Radicals Practice**Add or Subtract the Expressions Answer Answer Careful! and are NOT like terms! Simplify to first Home**Rational Exponents**• Radicals can be re-written with exponents: • Use properties of exponents to simplify expressions when appropriate. Example 3: Example 2: Example 1: Practice Home**Rational Exponents Practice**Simplify the Expressions Answer Answer Home**Solving Equations**Solving Equations with Exponents Solving Equations with Radicals • Step 1: Isolate the power • Step 2: Take the nth root of both sides of the equation (where n is the exponent). • Step 3: Solve further if necessary. • [If the exponent is a fraction, just raise both sides of the equation to the reciprocal power] • Step 1: Isolate the power • Step 2: Raise both sides of the equation to the nth power (where n is the index of the radical). • Step 3: Solve further if necessary. Always check your answer! Practice Home**Solving Equations Practice**Solve the Equations Answer Answer Don’t forget when taking the nth root and n is even! More Practice Home**More Solving Equations Practice**Solve the Equations Answer Answer Get the radicals on opposite sides of the equation and square each side. After isolating raise each side to the power. Home