Indices II — Paper 2 · IGCSE Mathematics 0580

16 Simplify 1  16 16  2 (a)  x  ,  81  Answer(a) [2] 16 y 10 × 4 y −4 (b) 7 . 32 y Answer(b) [2]

4 marks

Mark scheme: 4 4 16 (a) x8 2 B1 B1 x8 9 9 (b) 2y–1 2 B1 2 B1 y–1

This question in 0580/22 Oct/Nov 2010

18 Simplify the following. For Examiner's (a) (3x3)3 Use Answer(a) [2] 2 (b) (125x6) 3 Answer(b) [2]

4 marks

Mark scheme: 18 (a) 27x9 2 B1 kx9 or 27xn (b) 25x4 2 B1 kx4 or 25xn

This question in 0580/23 May/June 2011

17 (a) Simplify (3125t 125) 5. Answer(a) … [2] p 1 (b) Find the value of p when 3 = . 9 Answer(b) p = … [1] (c) Find the value of w when x72 ÷ xw = x8. Answer(c) w = … [1] __________________________________________________________________________________________

4 marks

Mark scheme: 17 (a) 5t25 2 B1 for 5tk or mt25 (m ≠ 0) (b) –2 1 (c) 64 1 M1 f 1458 3456

This question in 0580/22 May/June 2014

13 Simplify. (a) 12x12 ÷ 3x3 Answer(a) … [2] 1 (b) (256y 256 ) 8 Answer(b) … [2]

4 marks

Mark scheme: 13 (a) 4x9 final answer 2 B1 for answer kx9 or 4xk (k ≠ 0 ) (b) 2y32 final answer 2 B1 for answer ky32 or 2yk (k ≠ 0 )  1  2

This question in 0580/23 May/June 2015

1 Simplify. (x2) 5 … [1]

1 marks

Mark scheme: Question Answer Mark Part marks 1 x10 1

This question in 0580/21 May/June 2017

20 Simplify. (a) 6w0 … [1] (b) 5x3 − 3x3 … [1] (c) 3y6 # 5y-2 … [2]

4 marks

Mark scheme: 20(a) 6 1 20(b) 2x 3 final answer 1 20(c) 15y 4 final answer 2 B1 for 15 ky or ky 4 as final answer (k ≠ 0)

This question in 0580/23 May/June 2017

27 Simplify. 3 (a) 814 … [1] 2 4 (b) x 3 ' x - 3 … [1] 1 8 - 3 (c) 6 c y m

2 marks

Mark scheme: 27(a) 27 1 27(b) x2 final answer 1 1 2 −127(c) y 2 3  2   y 6  or 0.5y2 final answer 2 M1 for   or  2  or better  8   y  y 2 ky 2 or SC1 for answer or or c 2 y 2

This question in 0580/22 Oct/Nov 2017

21 Simplify. (a) ( 5x 4 ) 3 … [2] 3 8 (b) ( 256x 256 ) … [2]

4 marks

Mark scheme: 21(a) 125x12 2 B1 for 125xk or kx12 21(b) 8x96 2 B1 for 8xk or kx96

This question in 0580/22 May/June 2020

4 Simplify. a 2 ' a 6 … [1]

1 marks

Mark scheme: 4 1 1 a–4 or final answer a 4

This question in 0580/23 Oct/Nov 2020

11 Simplify 3x 3 # 4x 4 . … [2]

2 marks

Mark scheme: 11 12x 7 final answer 2 B1 for 12xj or kx7 (j,k ≠ 0) as final answer

This question in 0580/23 May/June 2021

7 Simplify. 32g 32 ' 4 g 4 … [2]

2 marks

Mark scheme: 7 8g 28 final answer 2 B1 for kg 28 or 8 g k as final answer or correct answer seen and spoilt

This question in 0580/23 Oct/Nov 2021

21 (a) 5 3 = 3h Write down the value of h. h = … [1] 3 (b) Simplify 4x 3 . ` j … [2]

3 marks

Mark scheme: 21(a) 1 1 oe 5 21(b) 64x9 2 B1 for 64 kx or kx 9 as final answer or correct answer spoiled

This question in 0580/22 Feb/March 2024

17 Find the value of 2 (a) 125 3 … [2] - 25 (b) 4 . … [2]

4 marks

Mark scheme: 17(a) 25 2 2 2 3 3 125 5 3 M1 for or 3 1252 or ( ) ( ) or B1 for 3 125 = 5 17(b) 1 2 1 1 [] M1 for or 32–1 or 32 2 5 1024

This question in 0580/22 May/June 2025