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Simplify Expressions in Exponential or Radical Form

Simplify Expressions in Exponential or Radical Form.

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Simplify Expressions in Exponential or Radical Form

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  1. Simplify Expressions in Exponential or Radical Form

  2. Focus 8 Learning Goal –(HS.N-RN.A.1 & 2, HS.A-SSE.B.3, HS.A-CED.A.2, HS.F-IF.B.4, HS.F-IF.C.8 & 9, and HS.F-LE.A.1)= Students will construct, compare and interpret linear and exponential function models and solve problems in context with each model.

  3. Review: • When we multiply powers of the same base, the exponents are added together. • So (91/2)(91/2) should be the same as 91/2+1/2 which is 91 or 9. • But, (3)(3) we also get 9. • Therefore, 91/2 must equal 3!

  4. A Few Rules… • You’re allowed to have exponents that are fractions! • The denominator of the fraction is the root. • A denominator of 2 means a square root. • A denominator of 3 means a cube root. • A denominator of 10 means a 10th root. • The numerator of the fraction is the power. • A number with 2/3s power is the cube root of the number squared.

  5. Definition of bm/n • For any nonzero real number b, and any integers m and n with n > 1,

  6. Practice #1 • Evaluate 1001/2 • The denominator is 2, take the square root of 100. • The numerator is 1, take it to the 1st power. • This means we are taking the square root of 100 to the 1st power. Which is the same as the square root of 100. • 1001/2 = 10 • Anything to the ½ power is just the square root of that number.

  7. Practice #2 • Evaluate 16 3/2 • The denominator is 2, take the square root of 16. • This equals 4. • The numerator is 3, take 4 to the 3rd power. • 163/2 = 64

  8. Practice #3 • Evaluate 1254/3 • The denominator is 3, take the cube root of 125. • This equals 5. • The numerator is 4, take 5 to the 4thpower. • 1254/3= 625

  9. Write the radical using rational exponents. • Since a radical is involved, the exponent will be a fraction. Remember: • The denominator is the root. • The numerator is the power. • In 4 is the root = denominator. • 1 is the power = numerator. • = x¼

  10. Practice #4 • In 3 is the root = denominator. • 2 is the power = numerator. • = y2/3

  11. Practice #5 • In 4 is the root = denominator. • 5 is the power = numerator. • = 135/4

  12. Apply More Exponent Properties • Simplify: • Same base, add the exponents. • 2/3 + 3/8 = 25/24

  13. Apply More Exponent Properties • Simplify: • Power to a Power = multiply the exponents • (2/3)(3/4) = (6/12) = ½ • y1/2

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