How do you simplify $(5 times 10^5)^-2$ ?

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Answer 1 · 2015-11-09T04:53:08

$(5 times 10^5)^-2= color(green)(4 times 10^-12$

We know that $color(blue)((ab)^m = a^m times b^m$

Hence $(5 times 10^5)^-2 = 5^-2 times (10^5)^-2$

We also know that $color(blue)((a^m)^n = a^(m*n)$

Hence $5^-2 times (10^5)^-2 = 5^-2 times 10^(5 times -2)$

$= 5^-2 times 10^-10$

$= (1/5^2) times (1/10^10)$

$= 1/(25*10^10)$

$= 100/(25 times 10^12)$

$= 4/10^12$

$= color(green)(4 times 10^-12$

How do you simplify (5 times 10^5)^-2 (5 times 10^5)^-2?