Examstyle Questions: Indices

a) Simplify t^{4} x t^{2}
(1 mark)
b) Solve
(i) 3(x  1) = x + 4
(3 marks)
(ii) 8x + 5 > 25
(2 marks)
c) Factorise 4x^{2}  25
(2 marks)
d) (i) Factorise x^{2} + 7x + 6
(ii) Hence solve the equation
x^{2} + 7x + 6 = 0
(1 mark)
(Marks available: 9)
Answer outline and marking scheme for question: 1
a) t^{6}
b) (i) x = 3.5
(ii) x > 2.5 (2^{4}/_{8} or better)
c) (2x + 5)(2x  5)
d) (i) (x + 1)(x + 6)
(ii) 1 and 6
(Marks available: 9)

Simplify:
(i) 5^{4} x 5^{3}
(ii) (3^{2})^{4}
(Marks available: 2)
Answer outline and marking scheme for question: 2
(i) 5^{4} x 5^{3} = 5^{4 + 3} = 5^{7}
(ii) (3^{2})^{4} = 3^{2 x 4} = 3^{8} = 6561
(Marks available: 2)