Indices

• Mastering the application of the 20 Rules of Indices

Rule 1: Product Law             Y^a x Y^b = Y ^a+b

Rule 2: Product coefficient law            My^a x Ny^b = MNy ^a+b

Rule 3: Quotient rule           Y^a ÷ Y^b = Y ^{a – b}

Rule 4: quotient – coefficient rule     My^a ÷ Ny^b = M ⁄ N Y ^{a – b}

Rule 5: Positive zero index           Y^o = 1, 10^o = 1, 2^o = 1

Rule 6: Negative zero index        -y^o = No solution, -19^o = No solution

Rule 7: Power of power index      (Y^a)^b = Y^ab

Rule 8: Other power of power index       (x^ay^b)^c = x^9c x y^bc = x^acy^bc

Rule 9: Negative index                    y^-1 =  1⁄y

Rule 10: Other Negative index      y^-x = 1⁄y^x

Rule 11: Other index rules (fractional index)    Y^1/x = x √Y

Rule 12: Negative power of power index           (y^a)^-b = 1 ⁄ Y ^ab

Rule 13: Other fractional index                       Y^a/x = ( x √Y)^a

Rule 14: Negative fractional index                 ( 1⁄y)^-1/x =   1⁄ x √ 1⁄y

Rule 15: Fractional power of power index     (a^x⁄b^y)^z = a^xz ⁄ b^yz

Rule 16: Other Negative fractional index       (x ⁄y)^-a/b   =  ( x √y ⁄x)^a

Rule 17: Reverse how of index                 y^a x y^b = y^a+b                  y^a ÷ y^b = y^{a -b}