How do you simplify and write #(-3m)^-4# with positive exponents?

Question

3437 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-15T12:39:38

See a solution process below:

First, use this rule of exponents to rewrite the terms within the parenthesis:

#a = a^color(red)(1)#

#(-3^color(red)(1)m^color(red)(1))^-4#

Next, use this rule of exponents to eliminate the parenthesis:

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

#(-3^color(red)(1)m^color(red)(1))^color(blue)(-4) => -3^(color(red)(1) xx color(blue)(-4))m^(color(red)(1) xx color(blue)(-4)) => -3^-4m^-4#

Now, use this rule of exponents to eliminate the negative exponents and complete the simplification:

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

#-3^color(red)(-4)m^color(red)(-4) => 1/-3^color(red)(- -4) * 1/m^color(red)(- -4) => 1/-3^4 * 1/m^4 => 1/81 * 1/m^4 => 1/(81m^4)#