Pure Mathematics · 2nd secondary · First Term

Exponents, Logarithms and their Applications — Rational exponents

About this lesson

This unit introduces rational exponents and the nth root, building on prior knowledge of square roots, cubic roots, and integer exponents. It covers the generalization of exponent laws to rational exponents, the definition and properties of the nth root (including cases for even/odd n and positive/negative a), and the rules for simplifying expressions with rational exponents and nth roots. The unit also includes solving exponential equations in R, with worked examples and exercises involving equations like x^(2/3)=128 and (2x+3)^(3/4)=81. Applications include geometry (sphere volume and radius) and using a calculator for approximations. By the end, students should be able to find nth roots, simplify expressions with rational exponents, apply exponent rules, and solve exponential equations in real numbers.

Main topics in this lesson

  • Rational exponents
  • nth roots
  • Properties of nth roots
  • Solving exponential equations in R
  • Simplifying expressions with rational exponents

Key terms and vocabulary

  • rational exponents
  • nth root
  • principle nth root
  • exponent laws
  • exponential equations
  • real roots
  • complex roots

Questions and answers on Exponents, Logarithms and their Applications — Rational exponents - practice and revision

Multiple choice questions on this lesson in Pure Mathematics for 2nd secondary, First Term, with practice exercises for revision and exam preparation.

1

باستخدام الآلة الحاسبة، القيمة التقريبية لـ 5^(1/3) لأقرب جزء من مائة هي

  • 1 1.71
  • 2 1.50
  • 3 2.24
  • 4 1.67
2

إذا كان حجم كرة يساوي (4/3)π وحدة مكعبة، فإن نصف قطرها يساوي

  • 1 1
  • 2 2
  • 3 3
  • 4 4
3

إذا كان حجم كرة يساوي 36π وحدة مكعبة، فإن نصف قطرها يساوي (باستخدام V = (4/3)πr^3)

  • 1 3
  • 2 9
  • 3 6
  • 4 27
4

مجموعة حل المعادلة (2x + 3)^(3/4) = 27 في R هي

  • 1 {39}
  • 2 {12}
  • 3 {18}
  • 4 {3}
5

مجموعة حل المعادلة x^(3/2) = 8 في R هي

  • 1 {4}
  • 2 {4, -4}
  • 3 {2}
  • 4 {16}
6

مجموعة حل المعادلة x^(2/3) = 9 في R هي

  • 1 {27, -27}
  • 2 {27}
  • 3 {3, -3}
  • 4 {9}

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