Indices questions - step by step pls?

Question

a) 12a^7/8 / 3a^1/4
b) (a^2/3 b^5/6)(a^1/2 b) / (ab)^1/3
c) (a^1/4 b^3)^1/2 / (a^1/3 b^1/4)^-5
d) (a^1/2 + a^1/2)(a^1/2 - a^1/2)

Answer 1

a)12a^7/8 / 3a^1/4
=(12/3)a^(7/8-1/4)
=4a^5/8

b)(a^2/3 b^5/6)(a^1/2 b) / (ab)^1/3
=a^(2/3+1/2-1/3) b^(5/6+1-1/3)
=a^5/6 b^11/6

c)(a^1/4 b^3)^1/2 / (a^1/3 b^1/4)^-5
=a^1/8 b^3/2 / a^-5/3 b^-5/4
=a^(1/8+5/3) b^(3/2+5/4)
=a^43/24 b^11/4

d)(a^1/2 + a^1/2)(a^1/2 - a^1/2)
=a^2(1/2)-a^2(1/2)
=0

Answer 2

Rules for Indices
Add when multiplying
Subtract when dividing

a) 4 a^(7/8) / a^(2/8) = 4 a^(5/8)

b)
a^(4/6) b^(5/6) a^(3/6) b / a^(2/6) b^(2/6)
a^(7/6) b^(11/6) / a^(2/6) b^(2/6)
a^(5/6) b^(9/6)
a^(5/6) b^(3/2)

c)
a^(1/8) b^(3/2) (a^(5/3) b^(5/4)
a^(43/24) b^(11/4)

d)
a - a + a - a = 0

Answer 3

Time's a wastin'! Sorry.