1. ## surds question

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

2. ## Re: surds question

Yes that's correct. Well done!

3. ## Re: surds question

Originally Posted by bigmansouf
(a) Find the value of n
(b) Write down the value of the expression
Find the value of n *what*?

There is no specified problem for (a). It could be
"Find the value of n which makes the exponent equal to zero."

4. ## Re: surds question

Originally Posted by greg1313
Find the value of n *what*?

There is no specified problem for (a). It could be
"Find the value of n which makes the exponent equal to zero."
Greg1313, You seemed to have missed the bit in red:

Given, when simplified the expression
(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

thank you