Any of these tools are good: Preplounge Mental Math, V. Cheng, Mimir Math.
It's more about the skills. I recommend to concentrate on the following:
1) Learn how to multiply double digit numbers (https://www.youtube.com/watch?v=6ndkkPZYJHo).
2) Learn how to work with zeros. You've mentioned - always use 10^power instead of zeros
300x9000 = 3*10ˆ2 x 9*10ˆ3=3x9*10ˆ(2+3)=27*10ˆ5
Handwritten it looks not that complicated. If you get used to writing all the numbers that way, you will never loose zeros and all multiplications/divisions will be replaced with + or -.
3) Learn the division table up to 1/11 (i.e. 5/6 = 83.3%). It will help you calculate any percentage problems