Tricks to solve surds and indices

  1. Laws of Indices:
    1. am x an = am + n
    2. am am – n
      an
    3. (am)n = amn
    4. (ab)n = anbn
    5. a n = an
      b bn
    6. a0 = 1
  2. Surds:Let a be rational number and n be a positive integer such that a(1/n) = aThen, a is called a surd of order n.
  3. Laws of Surds:
    1. a = a(1/n)
    2. ab = a x b
    3. = a
      b
    4. (a)n = a
    5. (a)m = am

1. (17)3.5 x (17)? = 178

2. Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to

3. If 5a = 3125, then the value of 5(a - 3) is:

4. (256)0.16 x (256)0.09 = ?

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

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