I am currently doing some algebra practice for English pre A Level Maths. I am doing examples of a worksheet and I am finding a few problems that have cropped up so far that I would greatly appreciate if someone could explain how to get the right solution as my algebra is pretty patchy in places and needs to be mastered!

Here are they are:

**Simplify the following expressions into their simplest form** **1,**
$\displaystyle {\frac {ab^2}{cd}} \times {\frac {ac^2}{bd}}$

I simplfied to:

$\displaystyle ={\frac {a^2bc}{d^2}}$

The answer in the back of the book:

$\displaystyle = a^2bcd^2$ ?

**2,**
$\displaystyle {[(ab)^3]^{-\frac {1}{2}}}$

I simplified to:

$\displaystyle =[a^3b^3]^{-\frac {3}{2}}$

Answer in the back of the book:

$\displaystyle =a^{-\frac {1}{2}}b^{-\frac {3}{2}}$ ?

**3,**
$\displaystyle (abc)^{\frac{1}{2}} \div (a^3b^3c^3)^{\frac {2}{3}}$

I simplified to:

$\displaystyle

={\frac {a^{\frac{1}{2}}b^{\frac{1}{2}}c^{\frac{1}{2}}} {a^2b^2c^2}}

$

The answer im the back of the book:

$\displaystyle

= a^{-\frac{3}{2}} b^{-\frac{3}{2}} c^{-\frac{3}{2}}

$ ?

Thanks in advance.

David