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

2 Answers
Jan 28, 2017

Answer:

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)#

Jan 28, 2017

Answer:

#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)#