Question

How do you simplify and write `(2b)^-5` with positive exponents?

Answer 1

See the entire simplification process below:

Explanation:

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

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

`(2b)^-5 = 1/(2b)^(- -5) = 1/(2b)^5`

Now, use these rules for exponents to complete the simplification:

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

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

`1/(2b)^5 = 1/(2^1b^1)^5 = 1/(2^(1 xx 5)b^(1 xx 5)) = 1/(2^5b^5) = 1/(32b^5)`

Answer 2

`1/(32b^5)`

Explanation:

Using the `color(blue)"laws of exponents"`

`color(red)(bar(ul(|color(white)(2/2)color(black)((ab)^m=a^mb^m ; a^-m=1/a^m)color(white)(2/2)|)))`

`rArr(2b)^-5=1/(2b)^5`

`=1/(2^5b^5)=1/(32b^5)`