Question

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

Answer 1

`4.2^-5 = 3125/4084101 ~~0.0076516`

Explanation:

`4.2 = 21/5`

`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`

`= 4084101`

`5^5 = 3125`

So `4.2^-5 = (21/5)^-5 = (5/21)^5 = 5^5/(21^5) = 3125/4084101`

`=1/1306.91232 ~~0.0076516`