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Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. GCSE Maths Starter 5 1) 5. Copy the shape below into your exercise books and draw 5 more shapes that tessellate with it.. 2. Increase £240 by 35%. 3. What is 159 x 72 4. Solve: 3(x+1) = 24 Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. • To find the value of calculations using indices. • To simplify letters and numbers when they are being X, +, -, ÷. • To use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, and of powers of a power EXTN: To simplify expressions with more than one letter and numbers. (Grade C) Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. • How can I simplify: 45 x 43? 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 48 • How can I simplify: 79 x 76? 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 = 715 Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. 26 x 2 4 24 x 2 2 = 210 = 26 35 x 3 7 = 312 General Rule: When multiplying terms with the same base, you add the powers EXAMPLE: 47 x 45 = 47+5 = 412 am x an = am+n Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. • How can I simplify 95 ÷ 93? 9x9x9x9x9 = 9 x 9 = 92 9x9x9 • How can I simplify 117 ÷ 112? 11 x 11 x 11 x 11 x 11 x 11 x 11 11 x 11 = 115 Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. 26 ÷ 2 4 25 ÷ 2 2 35 ÷ 3 7 = 22 = 23 = 3-2 General Rule When dividing terms with the same base, you subtract the powers EXAMPLE: 47 ÷ 45 = 47-5 = 42 am ÷ an = am-n Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. • How can I simplify 4 3 (4 ) ? 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 412 • How can I simplify 5 2 (7 ) ? 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 = 710 Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. (26)2 = 26 x 26 = 212 (35)3 = 35 x 3 5 x 3 5 = 315 General Rule: When raising a power to another power, you multiply the powers (am)n = am x n EXAMPLE: 5 7 (4 ) = 47 x 5 = 435 Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. • Simplify the following: 73 x 78 75 4 x 9 5 x 10 Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. • How can I simplify 5a3 x 6a7? 5xaxaxa x 6xaxaxaxaxaxaxa 5 x 6 x a x a x a x a x a x a x a x a x a x a = 30a10 Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 102/111. Lesson 5 Index Laws and Simplifying Algebra. Mathswatch 111. • To find the value of calculations using indices. • To simplify letters and numbers when they are being X, +, -, ÷. • To use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integer powers, and of powers of a power EXTN: To simplify expressions with more than one letter and numbers. (Grade C)