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

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

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Answer 1 · 2015-11-06T00:15:16

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

Explanation:

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

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

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

$= 4084101$ $= 4084101$

$5^{5} = 3125$ $5^5 = 3125$

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

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

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

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