Indices and standard form

# 5 10 3 000025 2500 can be written more simply as 4 10

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Unformatted text preview: 10 − 4 (d) 0.36 × 10 3 2.5 × 10 3 (2 × 10 ) × (2 × 10 ) 2 2 − 2.5 × 10 3 0.00025 2500 can be written more simply as 4 × 10 4 . Write the following values as simply as possible: (i) (3 × 10 ) × (2 × 10 ) (ii) 6 × 10 8 2 × 10 4 −2 2 (KS3/98/Ma/Tier 6-8/P1) 3.5 Fractional Indices Indices that are fractions are used to represent square roots, cube roots and other roots of numbers. a 1 2 = a for example, 9 3 a for example, 83 4 a for example, 625 4 n a 1 1 3 = 2 = 5 1 a4 = a = 1 a3 = 1 n 1 2 = 55 MEP Y9 Practice Book A 3.5 Example 1 Calculate: 1 1 (a) 81 2 (b) 1000 3 (c) 4 − 1 2 Solution 1 (a) 81 2 = 81 =9 (b) 1000 1 3 = 3 1000 = 10 (c) 4 − 1 2 1 = 4 1 2 1 4 = 1 2 = Exercises 1. Calculate: (a) 49 (d) 81 (g) 1 2 − (b) 1 2 92 64 (e) 100 (h) 36 1 2. − (c) − 1 2 1 2 16 1 2 − 1 2 (f) 25 (i) 144 2 1 Calculate: (a) (d) 3. 1 2 8 1 3 64 (b) 1 − 3 (e) 8 − 1 3 216 (c) 1 3 (f) 125 1 3 1000 000 − Calculate: (a) 32 (d) 81 1 5 − − 1 2 (b) 1 4 64 (e) 625 4 1 4 (c) 10 000 (f) 100 000 1 56 − 1 5 1 3 MEP Y9 Practice Book A 4. Calculate: 1 2 (a) (c) 5. 4 × 8 2 125 × 5 25 (b) (d) 625 5 1 2 1 (c) 1 3 1 16 2 = 8 (b) (d) 81 = 9 1 100 − (b) 1 3 16 4 = 2 (a 10 ) 1 2 1 2 = 10 Simplify: 1 (a) (c) (x 9 ) 3 − 1 2 a a 7. − 4 Is each of the following statements true or false: (a) 6. 1 9 × 27 3 (d) 1 2 a a Simplify: 3 (a) x2 x (b) 8. 3 x2 1 3 (c) x a a (d) a a 1 3 1 2 Calculate: − 1 2 (b) 1 0 9 + 9 2 (d) (9 − 9 0 ) 3 1 +42 (a) 4 (c) 1 256 2 1 1 2 57 1 2...
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## This document was uploaded on 03/03/2014 for the course O-LEVEL Mathematic at Beaconhouse School System.

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