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Simplify Expressions in Exponential or Radical Form

This learning goal focuses on constructing, comparing, and interpreting linear and exponential function models in high school algebra. Topics covered include rules for exponents, evaluating expressions with fractions, and simplifying expressions using exponent properties. Students will practice evaluating square roots, cube roots, and rational exponents. The content emphasizes understanding the relationship between bases, exponents, and roots when simplifying 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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