# Math Help - solve limit with high powers

1. ## solve limit with high powers

How do I calculate this limit?

2. Using L'Hospital's Rule... many times...

3. It is the only way?

4. No, you could also expand everything, then divide top and bottom by the highest power of $x$.

5. The limit will be $\left(\frac{3}{2}\right)^{20}$.

To see that notice that $(3x-1)^{20}=3^{20}x^{20}\left(1-\frac{1}{3x}\right)^{20}$.

6. I did it in a different, longer way.

(3x-1)^20 = ((3x-1)²)^10.

This way I've put the power of ten outside the whole expression and after a couple of lines ended up with (9/4)^10.

Your way is much shorter, I should notice such things in the future, thanks.