Curriculum
Pure Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
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Unit 2: Exponents and Logarithms
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Rational Exponents
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Rational Exponents — Lesson quiz
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The Exponential Function and Its Applications
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The Exponential Function and Its Applications — Lesson quiz
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Solving Exponential Equations
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Solving Exponential Equations — Lesson quiz
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The Inverse Function
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The Inverse Function — Lesson quiz
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The Logarithmic Function
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The Logarithmic Function — Lesson quiz
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Properties of Logarithms
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Properties of Logarithms — Lesson quiz
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Unit 3: Limits
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Unit 4: Trigonometry
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Text lesson
Rational Exponents
Rational Exponents
Laws of exponents
Laws of exponents
- The laws for integer exponents also hold for rational exponents
- provided the bases are positive:
| Law | Example |
|---|---|
| am × an = am+n | x1/2 × x3/2 = x2 |
| am ÷ an = am−n | x2 ÷ x1/2 = x3/2 |
| (am)n = amn | (a2/3)3 = a2 |
| (ab)m = am bm | (4y)1/2 = 2y1/2 |
- Be careful with negative numbers under even roots.
- The square root of a negative number is not a real number, so the general rules are applied only to positive bases.
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