The mathematics question is,
Simplify
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFUMUg84_GSwGJWUK2jxsZqNtxeaSS5PuHEiytkNP0hEhi6KRW8oNusGxkRfp7ZHtIO0Oe3lSJ5mz-9NtYaC19dJcWRLbFaEzX2dlVcQStLTzoExxHFTEDSlcinPoAojHjw5MQBVCXnfiy/s400/Question.jpg)
This question appears complex and quite intimidating.
Solution:
Let,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEAHUAISjDNiH4Xzzqv3MCmj1dCYuKtH4PSJ6bJg2S3pvrJRu91rq4mZGBhVpdErGajuHfH-EKmZpXM0jvWPQbW6oRW17F2oEZwGYUjFVynL3LUiqKDpC7gUmeBvykjFE6UZp2LotQn5Me/s400/Let+expression.jpg)
Substituting into the expression, we have,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3UOHl-j6RBbrhkSbc7rVxqtiB4G4TBXxz7wsmV4qGQlVWxCQbgn5KdAiAa9Bu3K-Lu3Hv22sNwnVK7evNm_WUWskW7lv1CjwIHZ4QpCd3D8CTwSerAYhznimlnkImcnL3RqHkzAsl73VR/s400/Substituting+into+expression.jpg)
Simplifying,
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiD3nKJg4rYYieDrFIGrLJmezQrwNN4MPdSaILt474t5ZVcV8-8aPEtoLuB99EjOXX7mBNXI4Mi6AwjERknTkwT27qAZpCuuTzF4XYsOIozMqkRIMD5arjyn9Ux62luyCT-9_ungv3X9FH1/s400/Simplifying+and+answer.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
Reference
http://www.intmath.com/Numbers/exp.gif
http://www.heymath.com/heymath/ (Login ID and Password required)
http://www.revisioncentre.co.uk/gcse/maths/indices3.gif