Worksheet 1
Exercise 1
Given that (3𝑝𝑝𝑞𝑞 2 )4 × 2𝑝𝑝�𝑞𝑞 8 = 𝑎𝑎𝑝𝑝𝑏𝑏 𝑞𝑞 𝑐𝑐 , find the values of the constants 𝑎𝑎, 𝑏𝑏 and 𝑐𝑐.         (3)
Exercise 2
           3𝑥𝑥
Given      34𝑦𝑦
                       = 27√3 , find 𝑦𝑦 as a simplified function of 𝑥𝑥.                               (3)
Exercise 3
(i) Given that 125√5 = 5𝑎𝑎 , find the value of 𝑎𝑎.                                                    (2)
                            16
(ii) Show that                    = 8 + 4√2
                           4−√8
      You must show all stages of your working.                                                       (3)
Exercise 4
Given that
                                                                        64𝑥𝑥 6
                                                                 𝑦𝑦 =          , 𝑥𝑥 > 0
                                                                         25
express each of the following in the form 𝑘𝑘𝑥𝑥 𝑛𝑛 where 𝑘𝑘 and 𝑛𝑛 are constants.
           1
(a) 𝑦𝑦 −2                                                                                            (3)
                   2
(b) (25𝑦𝑦)3                                                                                          (2)
Exercise 5
Simplify fully
               1   4
(a) �3𝑥𝑥 2 �                                                                                               (3)
       2𝑦𝑦 7 ×(4𝑦𝑦)−2
(b)           3𝑦𝑦
                                                                                                           (2)
Exercise 6
                                   20
(i) Show that √45 −                     + √6√30 = 5√5.                                                     (2)
                                   √5
                           17√2
(ii) Show that                    = 3√2 − 1.                                                               (3)
                           √2+6