Q:

Given, when simplified the expression

$\displaystyle (2x)^{-1}\times \frac{3}{\sqrt{x}}\times (6x^{n})^{2} $

independent of terms in x:

(a) Find the value of n

(b) Write down the value of the expression

My attempt:

part (a) $\displaystyle =(2x)^{-1}\times \frac{3}{\sqrt{x}}\times (6x^{n})^{2} $

$\displaystyle =\frac{1}{2x}\times 3x^{-\frac{1}{2}}\times 36x^{2n}$

$\displaystyle = 54 x^{2n-\frac{3}{2}}$

$\displaystyle 2n-\frac{3}{2} = 0 $

$\displaystyle n = \frac{3}{4}$

b) using part a

$\displaystyle = 54 x^{2n-\frac{3}{2}}$

sub n into the expression

$\displaystyle = 54 x^{(2(\frac{3}{4})-\frac{3}{2})}$

$\displaystyle = 54$

Please can someone check i don't know if I am right.

Thank you