How do you simplify #(2m^-4)/(2m^-4)^3# and write it using only positive exponents?

1 Answer
Feb 28, 2017

Answer:

See the entire solution process below:

Explanation:

First, we can simplify the denominator using these rules for exponents:

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

#(2m^-4)/(2m^-4)^3 = (2m^-4)/(2^color(red)(1)m^color(red)(-4))^color(blue)(3) = (2m^-4)/(2^(color(red)(1)xxcolor(blue)(3))m^(color(red)(-4)xxcolor(blue)(3))) = (2m^-4)/(2^3m^-12)#

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

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

#(2m^-4)/(2^3m^-12) = (2^color(red)(1)m^color(red)(-4))/(2^color(blue)(3)m^color(blue)(-12)) = (m^(color(red)(-4)-color(blue)(-12)))/(2^(color(blue)(3)-color(red)(1))) = (m^(color(red)(-4)+color(blue)(12)))/2^2 = m^8/4#