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#