How do you simplify #x^-5 / (2^(1/3)x ^-2)#?

1 Answer
Jun 7, 2016

Answer:

#1/(root(3)(2)x^3)#

Explanation:

You only need to use three things:

  • A negative exponent means the inverse of the positive exponent, so for example #3^(-2)=1/3^2#
  • A rational exponent #m/n# means that you have to take the #n#-th root of the #m#-th power, again as an example, #4^(5/2)=sqrt(4^5)#
  • The ratio between two powers of the same base is a power whose exponent is the difference of the exponents, so #a^3/a^2=a^(3-2)=a#

Put those things together and you have

#x^{-5}/x^{-2}=x^{-5+2}=x^{-3}=1/x^3#

#2^{1/3}=root(3)(2)#

And so, finally,

# x^{-5}/(2^{-1/3}x^{-2})= 1/(root(3)(2)x^3) #