What is the solution for x in 2x^(1/4) = 64/x using indices?

[Mo]

Indices.Again i think I've got close to the answer, it just does not want to show its self! A push in the right direction would be appreciated ... here's the problem:

$$2x^ \frac{1} {4} = \frac{64} {x}$$

Regards
Mo

 

[Muzza]

Multiply both sides by x. Remember that x = x^1 and x^a * x^b = x^(a + b) for all a, b.

 

[Mo]

Hmm i multiplied both sides by x ..i think the answer is:

$$2x^ \frac{2} {4} = 64$$ right?? ... carrying on ...

then divide both sides by 2 ..so we are left with ..

$$x ^\frac {2} {4} = 32$$

am i along the right lines here??

 

[Hurkyl]

How did you get $x^{2/4}$?

 

[Mo]

hmm, i multiple both sides by x so

$$2x^ \frac {1} {4} X x = 2x^ \frac {1} {4} X x^1$$

and since we add the indices when multiplying i get 2 no?

 

[Mo]

oh lol i think i just spotted it ..

 

[Mo]

edit: should be 1.25 right?

Ack - stupid mistakes , i got it now.Completely overlooked it .. .

Thanks both