How do you simplify #(9/2)^-1#?

1 Answer
Jun 18, 2018

Answer:

See a solution process below:

Explanation:

There are a couple of ways we can do this. The first is to use these two rules of exponents:

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

#(9/2)^color(red)(-1) => 1/(9/2)^color(red)(- -1) => 1/(9/2)^color(red)(1) => 1/(9/2) => 2/9#

Another way is to use these rules of exponents:

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

#(9/2)^color(red)(-1) => 9^color(red)(-1)/2^color(red)(-1) => 9^color(red)(-1) xx 1/2^color(red)(-1) => 1/9^color(red)(- -1) xx 2^color(red)(- -1) => 1/9^color(red)(1) xx 2^color(red)(1) => 1/9 xx 2 => 2/9#