Indices and Exponential Graphs Learning Outcomes I can add, subtract, multiply and divide terms containing indices I can calculate with negative indices I can calculate with fractional indices and represent as roots I can write very large and very small numbers in standard form I can add, subtract, multiply and divide in standard form I can solve equations with indices I can recognise and draw graphs of exponential functions, y=aⁿ, y=a-ⁿ I can use exponential graphs in real life situations Approx Time: 3 periods

Indices Indices am x an = am+n (add indices when multiplying) 1) x2 x x8 = 2) x5 x x-2 = am ÷ an = am-n (subtract indices when dividing) 1) x6 ÷ x4 = 2) 30x5 ÷ 10x-2 = (am)n (when we have a number in index form raised to a power we multiply the indices) 1) (x2)5 = 2) (3x3)2 = 3) (4x2y3)3 = a0 = 1 (any number t the power of 0 is equal to 1) 1) x0 = 2) p0 =

Applying the Laws of Indices b) 8 1/3 c) 32 1/5 d) 43/2 e) 8 5/3 f) 32 4/5 g) 16 3/4 N N2 N3 N4 N5 1 2 4 8 16 32 3 9 27 87 243 64 5 25 125 6 36 216 You need to know:

Negative Indices Indices Rule: a-n = 1 an To evaluate a number in index form with a negative index, You simply turn the term upside down and remove the minus sign a) 25 -3/2 b) 0.008 -2/3

Indices Additional Notes

                Indices and Exponential Graphs Learning Outcomes: At the end of the topic I will be able to Can Revise Do Further   I can add, subtract, multiply and divide terms containing indices I can calculate with negative indices I can calculate with fractional indices and represent as roots I can write very large and very small numbers in standard form I can add, subtract, multiply and divide in standard form I can solve equations with indices I can recognise and draw graphs of exponential functions, y=aⁿ, y=a-ⁿ I can use exponential graphs in real life situations         Approx Time: 3 periods      