Maths Question ( Laws of Indices ) thx :)

1. [ 3a^2 . b^-1 . (6a^-3 . b^-2)^-2 ]^-3

= ( 3a^2 . b^-1 . 6a^6 . b^4 )^-3

= ( 18a^8 . b^3 )^-3

= 18a^-24 . b^-9


2. (4x^-100 . y^501)^-2 / (8^-2 . x^250 . y^1000)

= ( 4x^200 . y^-1002 ) / (1/64 . x^250 . y^1000 )

= 64 (4y^-2002) / (x^50)

= 256x^-50 . y^-2002


3. (16a^-3 / 8^-1 . ab^-2) * [(4^-3 . a^2 . b^-5) / (-2a)^2 ]

= ( 128a^-2 . b^2 ) * [ 4^-4 . b^-5 ]

= 0.5a^-2 b^-3


4. [(-16a^-6 . b^7) / (2^3 . a^-5 . b^10 . c^-2)] ^-3

= (-16^-3 . a^18 . b^-21) / (2^-9 . a^15 . b^-30 . c^6)

= -16^-3 . a^3 . b^9 . c^-6

= -a^3 . b^9 / 4096c^6


5. [(25m^2 n^-3) / (5^4 m^-5 n^2)] ^-2

= (25^-2 . n^6) / (5^-8 . m^10 . n^-4)

= 625n^10 . m^-10

1. [ 3a^2 . b^-1 . (6a^-3 . b^-2)^-2 ]^-3

= ( 3a^2 . b^-1 . 6a^6 . b^4 )^-3

= ( 18a^8 . b^3 )^-3

= 18a^-24 . b^-9


2. (4x^-100 . y^501)^-2 / (8^-2 . x^250 . y^1000)

= ( 4x^200 . y^-1002 ) / (1/64 . x^250 . y^1000 )

= 64 (4y^-2002) / (x^50)

= 256x^-50 . y^-2002


3. (16a^-3 / 8^-1 . ab^-2) * [(4^-3 . a^2 . b^-5) / (-2a)^2 ]

= ( 128a^-2 . b^2 ) * [ 4^-4 . b^-5 ]

= 0.5a^-2 b^-3


4. [(-16a^-6 . b^7) / (2^3 . a^-5 . b^10 . c^-2)] ^-3

= (-16^-3 . a^18 . b^-21) / (2^-9 . a^15 . b^-30 . c^6)

= -16^-3 . a^3 . b^9 . c^-6

= -a^3 . b^9 / 4096c^6


5. [(25m^2 n^-3) / (5^4 m^-5 n^2)] ^-2

= (25^-2 . n^6) / (5^-8 . m^10 . n^-4)

= 625n^10 . m^-10


so easy !! YEAR!