1. ## Simplifing

How do i simplify with out the calc on these examples?

$81^{3/4}$

$ln 9 - 4ln3$

$\frac{200}{\sqrt5}$

$\sqrt{432}$

Thank you

2. $81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}}=3^{4\cdot\fra c{3}{4}}=3^3=27$

$\ln 9-4\ln 3=\ln 3^2-4\ln 3=2\ln 3-4\ln 3=-2\ln 3$

$\frac{200}{\sqrt{5}}=\frac{200\sqrt{5}}{5}=40\sqrt {5}$

$\sqrt{432}=\sqrt{2^43^3}=4\cdot3\sqrt{3}=12\sqrt{3 }$

Edited. You're right songoku

3. Originally Posted by red_dog
$\sqrt{432}=\sqrt{2^43^3}=16\cdot3\sqrt{3}=48\sqrt{ 3}$
A little correction : 16 should be 4 ^^