1. ## [SOLVED] 4x^23+769=347389

Hi i have this problem.... Well this is a made up problem so i can attempt to get the real one my self.. I feel sort of dumb because i don't know this one...

4x^23+769=647389....

My problem is- I don't know what to do with the ^23... how do i get it over the equals..... IF that is what you do.......

4x^23=646620

4x= ?????

x= what ever ????/4

2. $\displaystyle 4x^{23}+769=647389$

$\displaystyle 4x^{23} = 646620$

You divide both sides by 4 FIRST. As with any algebra problem, you try to isolate x as much as possible before performing whatever operation you need.

$\displaystyle x^{23} = 161555$

Now, using your calculator you would take the 23rd root of both sides to get rid of the exponent just like you would take the square root of both sides if the x was squared.

$\displaystyle \sqrt[23]{x^{23}} = \sqrt[23]{161555}$

$\displaystyle x \approx 1.684$

You would need to know how to use your calculator to use that function. If not, you can always use the relation:

$\displaystyle a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = \left(\sqrt[n]{a}\right)^{m}$

So going back to $\displaystyle x^{23} = 161555$ , raise both sides by $\displaystyle \frac{1}{23}$:

$\displaystyle \left(x^{23}\right)^{\frac{1}{23}} = 161555^{\frac{1}{23}}$

That may be easier to punch in your calculator?

3. Thank you!

We are not allowed to use cal.......

Kyle