F.1 math(difficult question)

1a)
-8^4 = (-8^2)^2
=(64)^2
=64 x 64
=4096

or

-8^4 = (-2^3)^4
=(-2)^12
=4096

1b)
(2^6)^5 = 2^30
(2^7)^4 = 2^28

therefore
(2^6)^5/(2^7)^4
=2^30/2^28
=2^2
=4

2a)
=4 cages x 4 types x 4 animals
=4^3 animals

2b)
=4^3 animals x 4 legs
=4^4 legs

3)
refer to website

1.Without using calculators,find the values of the following:
(a) -8^4
=-8*-8*-8*-8
=64*-8*-8
=-512*-8
=4096

(b) (2^6)^5/(2^7)^4
=2^30/2^28
=2^2/2
=4/2
=2

2.There are 4 cages in garden A,each cage can keep 4 types of animals,each type has 4 animals,each animals has 4 legs.Use index notation to express the total number of the following in garden A.Then find their values.
(a)animals=4 cages * 4 types *4 animals=4^3 animals
(b)legs=4 cages * 4 types *4 animals* 4 legs=4^4 legs

3.In the question No2,What the meaning of notation??
記數法