![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAW8l4kg_dPKEy0eTqQomwqzdBVPtiIJZS2zESTH3LZ4woYGVXlJQlQrAG7KKBTmipBwj0ApB94QYckzzWppVUNBHGqZY4ZDpsZAac15c_VGrmWNvyah5ow7RkLsjwkRLASxY6737iOhas/s400/bavarian-scenery.gif)
Picture is from http://www.wistfullywandering.co.uk/germany.htm
Germany in spring (Bavarian countryside)
Now for mathematics question.
Simplify:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglSrvzwrMOrwYyvVeSeAOdmDk1ve6sAydFssmcHwCqBMBc4y5cZ58If5ZOhwl0lIPmC9-TpkRopti3prtnqfXWZo32nbcjOMmFFOl3wV_VYuY3eXHyIy0kFRqzY3STU7Mq1iHkXsgFTuLX/s400/Simplify+question.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgFW2BHTOqAU5rtMUqs45u6sBfoh4QOqxwW4x_85XY8YGzkKy12U_nhumB5iDD6qfPfAZSefxR1ZWEBVua_FnXwF4DorCfhRwyGKldFXyaRxu-FU0eU6-ioZDGO5PT5t9h3X1xtNVsUNtx/s400/math-problems.gif)
Extracted from http://eppsnet.com/images/math-problems.gif
Titled: Our Kids are Smater Than Yours
Solution:
Using algebraic expanding, we have the following,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBxJbqu1rKXyEhxSf9mG_b-MYG-mFuENzkevFjzvFgoVk7_Cr3On-uGfxOm79xEEeEIKk4y5oxtlcY47uupw-K1CZzbUodBIqQDKr01Vi7qB8pLEFVyrDKSSP2YysurSYt4DfjaNm4eJk7/s400/Solution.jpg)
After simplifying,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgj9UYv4xKoqkYPz6tEFc70-fvHzpxQvzgGGKAn2Y0XXD4VNZrY1QSHcutQIWbiSg0SSN9jCxGgeKzR0QbCA-5LlbIbaqlUyH2a6qm7G5zu8qx0NMu-QvlokusZc55Y5TlgIiWP9Wr_Mpeb/s400/Results.jpg)
Summary of Index Laws
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX3jVjRxWZy9isDQBYZouS98-Sza3KolRFO_03zTjsFRAKCOfMZYzB0VRCsfkhIlWEXV2v-idKgIBA5ElMzXnNiNRwecozN2ALFC3nECdWAhquKH3JUomZrxC_mQARncwgeKyXxF8BvZKh/s400/exp.gif)
The laws are obtained from http://www.intmath.com/Numbers/exp.gif
Another representation of Index Rules
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQdsDYaDYmm_H2q-cYoSWnfXIfwfdnxPXtS72VCPL5Hy2Xvo7dc9MwzSM-A-7I259JXO2dD5HJ2nJMtlrnJEvX3pqAKNlTtbZQ1VRU6j60zQf5H8iEpwV7hiMb3UEpoEhD-kGVRj3C9AFb/s400/indices3.gif)
The Rules are obtained from http://www.revisioncentre.co.uk/gcse/maths/indices3.gif
Copyright © Matthew Pinkney 2003
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxrbW-rhRWTtqMNQlppdttXXOv5o6NT8zCEV6jh_lE9qRRBRIOrogaoFTZN6elwZdVK1yGhFBbrT7ZXNRarUEdExbXbDLXO7mMaDMGHlDM2FigPw1XKcrDTs1aFVUZjW47GWU-aU5-JBme/s400/scenery6.jpg)
Kampong days environment. Any study or homework will make me remember this type of ambient surrounding.
Reference
http://www.intmath.com/Numbers/exp.gif
http://www.revisioncentre.co.uk/gcse/maths/indices3.gif
http://www.wistfullywandering.co.uk/bavarian-scenery.gif
http://www.wistfullywandering.co.uk/germany.htm
http://www.cescg.org/CESCG-2002/photos/scenery/scenery6.jpg
http://eppsnet.com/images/math-problems.gif