# A problem with fractional indices

• Sep 11th 2007, 04:31 AM
Coach
A problem with fractional indices
I tried to solve the following problem

$x^{\frac{1}{2}}=2x^\frac{3}{4}$

I tried raising the left hand side to the second power in order to mkae the left hand side x.

But I still couldn't solve it.

Thank you!
• Sep 11th 2007, 04:39 AM
topsquark
Quote:

Originally Posted by Coach
I tried to solve the following problem

$x^{\frac{1}{2}}=2x^\frac{3}{4}$

I tried raising the left hand side to the second power in order to mkae the left hand side x.

But I still couldn't solve it.

Thank you!

$x^{\frac{1}{2}}=2x^\frac{3}{4}$

Try raising it to the 4th power instead:
$\left ( x^{\frac{1}{2}} \right )^4 = \left ( 2x^\frac{3}{4} \right ) ^4$

$x^2 = 2^4 x^3$

and go from there.

Hint: When you have an equation with a fractional denominator n/m, raise both sides of the equation to the mth power.

-Dan