Roots Powers Sf

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Roots, powers and standard form Cube roots 1. Find the cube root of 8 (the cube root of 8 can be written as

3

8)

Complete …… × …… × …….. = 8 So,

2. Find

3

3

8 = ……..

9

3. Label the diagram with theses words: base, index

6³

4. Calculate 24

24 = ….. × …….×……×……× = …….

5. Calculate 5³

6. Calculate 45

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7. Calculate 24 × 2³

……× …… × ….. × ……. × ……× ……×…… = 2 …… OR 2 ( …… + …….) = 2 ……

8. Calculate the following: (a) 103 × 104

(d) 10-3 × 102

(b) 63 × 65

(e) 53 × 5-3

(c) 82 × 84

(f) x3 × x4

9. If (a)

p = 5 × 103 q = 4 × 104 Find the value of p × q.

5 × 103 × 4 × 104 = 5 × 4 × ……. × ……… = …..…. × 10 …………. In standard form = ……… × 10 ………….

(b)

Find the value of p + q.

p = 5 × 103 = …….. × 104 q = 4 × 104 p+ q=

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10. If

p = 6 × 104 q = 3 × 105

(a)

Find the value of p × q.

(b)

Find the value of p + q.

(c) Find the value of

p . Give your answer in standard form. q

(d) Find the value of

q . Give your answer in standard form. p

11. (a) Write 63 000 000 in standard form.

(b)

Work out 63 000 000 multiplied by 2 × 10³ Give your answer in standard form.

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12. Place these numbers in ascending (increasing) order 5100

5.1 × 10²

0.51

5.1 × 10-2

51

5.1

13. (a) Write down 0.000 345 in standard form

(b) Work out 0.000 345 × 2 × 10³

14. Write down the following in standard form: (a) 1760

(e) 0.5

(b) 1 760 000

(f) 0.0078

(c) 89 763 200

(g) 0.00000065

(d) 10 900 000 000

(h) 0.000 000 09

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