Indices and Surds

Indices and Surds

1. Indices

   • Multiplication Rule
     • x^a * x^b = x^a+b
     • e.g. 2^2 * 2^3 = 2^5 = 32
   • Division Rule
     • x^a / x^b = x^a-b
     • e.g. 2^3 / 2^2 = 2^1 = 2
   • Power on Power Rule
     • (x^a)^b = x^a*b
     • e.g. (2^3)^2 = 2^3*2 = 2^6 = 64
   • Power of Zero
     • x^0 = 1
     • e.g. 2^0 = 1
   • Negative Powers
     • x^-a = 1/x^a
     • e.g. 2^-2 = 1/2^2 = ¼
   • Fractional Indices
     • x^a/b = (b√(x))^a
     • e.g. 8^2/3 = (cube √(8))^2 = 2^2 = 4

2. Surds

   • Addition
     • a*√(b) + c*√(b) = (a+c)*√(b)
     • e.g. 4*√(7) + 3*√(7) = 7*√(7)
   • Subtraction
     • a*√(b) - c*√(b) = (a-c)*√(b)
     • e.g. 4*√(7) - 2*√(7) = 2*√(7)
   • Multiplication Rule
     • √ab = √a * √b
     • e.g. √2*4 = √2*√4 = 2√2
   • Division Rule
     • √a/b = √a / √b
     • e.g. √2/3 = √2 / √3
   • Rationalising the Denominator
     • a / √b * √b / √b = a√b / b
       • e.g. 1 / √2 * √2 / √2 = √2 / 2
     • a / b+√c * b-√c / b-√c = a(b-√c) / (b+√c)(b-√c)
       • e.g. 1 / 2+√2 * 2-√2 / 2-√2 = 2-√2 / 4-2 = 2-√2 / 2