How do you find the value of #125^(-2/3)#?

Question

1733 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-11T12:14:33

See the entire solution process below:

First, we can rewrite this expression using this rule of exponents:

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

#125^(-2/3) = 125^(color(red)(1/3) xx color(blue)(-2)) = (125^color(red)(1/3))^color(blue)(-2)#

We can next rewrite the term inside the parenthesis using this rule for exponents and radicals:

#x^(1/color(red)(n)) = root(color(red)(n))(x)#

#(125^color(red)(1/color(red)(3)))^color(blue)(-2) = (root(color(red)(3))(125))^color(blue)(-2) = 5^color(blue)(-2)#

Now, use this rule of exponents to complete the evaluation:

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

#5^color(blue)(-2) = 1/5^color(blue)(- -2) = 1/5^2 = 1/25 = 0.04#