Exponents

Unit 2 Exponents Curriculum Statement Revise all laws of exponents learnt in Grade 9 Use the laws of exponents to simplify expressions and solve equations.

Table of contents Applications of Laws of Exponents Solving Exponential Equations Multiplication and Division of Polynomials with one or more terms

Exponential Laws

Applications of Laws

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Examples

Test your knowledge

Question Simplify - ( - 3 )2 Answer A)9B) - 9 C) - 6D) 6

Exponential Equations An equation of the type: a x = b is called a exponential equation. There are two methods to solve exponential equations. 1. Write the equation in the form a x = a b then make use of the fact that x = b or 2. Write the equation in the form a x = k, if k is not a power of a, then use the trial and improvement method to find an approximate solution for x.

Exponential Equations

Test your knowledge Question Solve for x: (-3) x = 9 Answer A)2B) - 2 C) 3D) -3

Test your knowledge Question Solve for x: x 4 =16 Answer A)±2 B) 2 C) -2 D) No Solution

Simplify expressions using Laws One term: Factorise the bases into prime factors and simplify. More than one term in the numerator or denominator: Factorise the bases into prime factors simplify and factorise.

Multiplication and division with one term 1. Example One term: Factorise the bases into prime factors and simplify.

Multiplication and division with more than one term Example More than one term in the numerator or denominator; Factorise the bases into prime factors Simplify and factorise

Test your Knowledge Question Simplify 5 2n+1.5 2n n-2 Answer A)5 B) 10 C) 25 D) 15

Test your Knowledge Question Simplify 3 n + 3 n+2 3 n-1 Answer A)15 B) 10 C) 30 D) 9