How do you simplify #(2a^-2)/(2a)^-3#?

1 Answer
Mar 12, 2017

Answer:

See the entire solution process below:

Explanation:

First, use these rules for exponents to simplify the denominator:

#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(2a^-2)/((2a)^-3) = (2a^-2)/((2^color(red)(1)a^color(red)(1))^color(blue)(-3)) = (2a^-2)/((2^(color(red)(1)xxcolor(blue)(-3))a^(color(red)(1)xxcolor(blue)(-3)))) = (2a^-2)/(2^-3a^-3)#

We can now use these three rules for exponents to complete the simplification:

#a = a^color(red)(1)# and #a^color(red)(1) = a# and #x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#(2a^-2)/(2^-3a^-3) = (2^color(red)(1)a^color(red)(-2))/(2^color(blue)(-3)a^color(blue)(-3)) = 2^(color(red)(1)-color(blue)(-3))a^(color(red)(-2)-color(blue)(-3)) = 2^(color(red)(1)+color(blue)(3))a^(color(red)(-2)+color(blue)(3) = #

#2^4a^1 = 16a#