# What is the value of: 4.2 to the negative fifth power?

Nov 6, 2015

${4.2}^{-} 5 = \frac{3125}{4084101} \approx 0.0076516$

#### Explanation:

$4.2 = \frac{21}{5}$

${21}^{5} = {\left(20 + 1\right)}^{5} = {20}^{5} + 5 \cdot {20}^{4} + 10 \cdot {20}^{3} + 10 \cdot {20}^{2} + 5 \cdot 20 + 1$

$= 3200000 + 800000 + 80000 + 4000 + 100 + 1$

$= 4084101$

${5}^{5} = 3125$

So ${4.2}^{-} 5 = {\left(\frac{21}{5}\right)}^{-} 5 = {\left(\frac{5}{21}\right)}^{5} = {5}^{5} / \left({21}^{5}\right) = \frac{3125}{4084101}$

$= \frac{1}{1306.91232} \approx 0.0076516$