How do you solve x^ (-2/3) = 9?

2 Answers
May 11, 2018

raise both sides to the -3/2 power.

Then you have:
x^((-2/3)(-3/2))=9^(-3/2)

x=9^(-3/2)=(3^2)^(-3/2)

x= 3^-3

x=1/27

May 11, 2018

A trick using logs.

x=1/27

Explanation:

Given: x^(-2/3)=9

Take logs of both sides:

ln(x^(-2/3))=ln(9)#

-2/3ln(x)=ln(9)

ln(x)=-3/2ln(9)

x=ln^(-1)[-3/2ln(9)]

x= 0.037color(white)(.)bar(037)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1000x=37.037bar(037)
ul(color(white)(1000)x=color(white)(0)0.037bar(037)larr" Subtract")
color(white)("d") 999x=37

x=37/999 = 1/27
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Check")

x^(-2/3) = 1/(x^(2/3))

Consider x^(2/3)->(1/27)^(2/3)= 0.11bar1

1/(x^(2/3))=1/(0.11bar1) = 9 color(red)(larr" As required")