數學-指數,根式唔識help!!急~.

18)
√(a)b / (a√b)^(-3/2)
= a^(1/2) * b * a^(-1 * -3/2) * b^(-1/2 * -3/2)
= a^(1/2) * b * a^(3/2) * b^(3/4)
= a^(1/2 + 3/2) * b^(1 + 3/4)
= a^2b^(7/4)

19)
(a/b)^(3/2) * (b/a)^(1/2) / (a/b)^(-3/6)
= a^(3/2) * b^(-3/2) * b^(1/2) * a^(-1/2) * a^(3/6) * b^(-3/6)
= a^(3/2 - 1/2 + 1/2) * b^(-3/2 + 1/2 - 1/2)
= a^(3/2)b^(-3/2)
= a^(3/2)/b^(3/2)

20)
x√(y^3) / √(x√y)
= x * y^(3/2) * x^(-1/2) * y^(-1/4)
= x^(1 - 1/2) * y^(3/2 - 1/4)
= x^(1/2)y^(5/4)

22)
16^(k - 1) / (^4√(256^(k - 2)) * 8^(-k))
= 2^(4k - 4) / (2^(2k - 4) * 2^(-3k))
= 2^(4k - 4) * 2^(-2k + 4) * 2^(3k)
= 2^(4k - 4 - 2k + 4 + 3k)
= 2^(5k)
= 32^k

23)
(a^(1/3) - 1)(a^(2/3) + a^(1/3) - 1)
= a^(1/3) * (a^(2/3) + a^(1/3) - 1) - (a^(2/3) + a^(1/3) - 1)
= a + a^(2/3) - a^(1/3) - a^(2/3) - a^(1/3) + 1
= a - 2a^(1/3) + 1

28)
(√63 - √3)(3√7 - √12)
= (3√7 - √3)(3√7 - 2√3)
= 9(7) - 3√21 - 6√21 + 2(3)
= 63 + 6 - 9√21
= 69 - 9√21

29)
(4√5 + √3)(√5 - 4√3)
= 4(5) + √15 - 16√15 - 4(3)
= 20 - 12 - 15√15
= 8 - 15√15

34)
a.
(1 + √2 + √3)(1 + √2 - √3)
= ((1 + √2) + √3)((1 + √2) - √3)
= (1 + √2)^2 - (√3)^2
= 1 + 2√2 + 2 - 3
= 2√2

b.
1/(1 + √2 + √3)
= 1/(1 + √2 + √3) * (1 + √2 - √3)/(1 + √2 - √3)
= (1 + √2 - √3)/(2√2)
= (2 + √2 - √6)/4