Question

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

Answer 1

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)`