Math Lesson 3:
Exponents and Surds
The Number System
This section covers the fundamental concepts of the number system, including natural numbers, integers, rational numbers, and irrational numbers.
Exercise: Number Classification
Classify √2. Is it Rational or Irrational?
Working with Irrational Numbers (Surds)
Surds are irrational numbers that are roots of rational numbers. We can simplify them by finding perfect square factors.
Exercise: Simplifying Surds
Simplify √12 (Format example: 2√3):
Laws of Exponents
Exponents follow specific laws for multiplication, division, and powers. For example, $x^a \cdot x^b = x^{a+b}$.
Exercise: Exponent Laws
Simplify (z⁴)²:
Exponential Equations
To solve exponential equations, we try to make the bases on both sides the same.
Exercise: Solving for x
Solve for x: 2x = 16
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