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

1 Answer
Nov 9, 2015

Answer:

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

Explanation:

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#