Prime factorisation, indices and standard form - some great questions

As we all know by now (in England anyway) the new GCSE in maths is going to require pupils to make links between areas of maths, and challenge pupils to apply understanding in ways they might not have previously. In writing the new homework booklets for my department I have been challenging myself to ask questions in this vein, and have found a rich source in linking prime factorisations, indices and standard form. Now admittedly there are already related topics, however I think that I have developed some questions that challenge pupils understanding of these topics in ways that perhaps haven't been used as frequently before now. Here I am sharing a run-down of my top seemingly straightforward questions (in no particular order):

1) 108 = 2² × 3³. 108² = 11664. Find the prime factorisation of 11664.

2) 9216 = 2¹⁰ × 3². Find the value of √9216.

3) Calculate (3 x 10⁴)³, giving your answer in standard form.

4) Find the prime factorisation of 6 x 10⁴, giving your answer in index form.

5) Find the prime factorisation of 3.2 x 10⁷, giving your answer in index form.

6) Find √(1.6 x 10⁵), giving your answer in standard form.

7) Calculate √(1/25), giving your answer in standard form.

8) Calculate (1.25 x 10⁸)^(2/3), giving your answer in standard form.

These and more will be in my term 2 homework booklet for the pupils aiming at grades 7+ on the new GCSE, and I think are precisely the sort of skills that the new GCSE is aimed at ensuring pupils develop.