if sqrt 3 5 xx 92 3a 3sqrt then a, Surds and Indices, General Mathematics

Question:If` (sqrt(3))^5 xx 9^2 = 3^a xx 3sqrt(3),` then a equals :

A 2 
B 3 
C 4 
D 5

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+ AnswerD

+ Explanation`(sqrt(3))^5 xx 9^2`

`= 3^a xx 3sqrt(3) =>(31^(1∕2)^5 xx (3^2)^2`

`= 3^a xx 3^1 xx 3^(1/2)`

`:. 3^(5∕2) xx 3^4`

`= 3^a xx 3^1 xx 3^(1∕2) or 3^(5/2 + 4)`

`= 3^((a + 1 + 1/2))`

`or 3^(13∕2)`

`= 3^(a + 3/2). So, a + 3/2`

`= 13/2 or a = (13/2 - 3/2)`

`= 5 `

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