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# How do you simplify e^(-2ln5)?

May 30, 2017

0.04

#### Explanation:

We have,

${e}^{- 2 \ln 5} = {e}^{\ln \left({5}^{-} 2\right)} = {5}^{-} 2 = \frac{1}{5} ^ 2 = \frac{1}{25} = 0.04$

Using the following properties of logarithms and exponentials,

$1.$ $n \cdot \ln$ $\left(m\right) = \ln$ $\left({m}^{n}\right)$ ; $\textcolor{b l u e}{H e r e}$ $\textcolor{b l u e}{P u t}$ $\textcolor{b l u e}{n = - 2}$ $\textcolor{b l u e}{\mathmr{and}}$ $\textcolor{b l u e}{m = 5}$

and

$2.$ ${e}^{\ln \left(a\right)} = a$ ; $\textcolor{b l u e}{H e r e}$ $\textcolor{b l u e}{P u t}$ $\textcolor{b l u e}{a = {5}^{-} 2}$