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

1 Answer
Apr 23, 2017

Answer:

See the entire solution process below:

Explanation:

First, use this rule of exponents to eliminate the negative exponent:

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

#(2m)^color(red)(-3) = 1/(2m)^color(red)(- -3) = 1/(2m)^3#

Next, use these two rules of exponents to complete the simplification:

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

#1/(2m)^3 => 1/(2^color(red)(1)m^color(red)(1))^color(blue)(3) => 1/(2^(color(red)(1) xx color(blue)(3))m^(color(red)(1) xx color(blue)(3))) => 1/(2^3m^3) => 1/(8m^3)#