x^(-n) = 1 / x^n
So x^-⅔ = 9 is equal to:
x^⅔ = 1 / 9
Rise both sides to pover of three.
x^2 = 1 / 9^3
x^2 = 1 / 729
x = ± 1 / √729
x = ± 1 / 27
You must eliminate the solution
x = - 1 / 27 because
x^⅔ = √x^3
In this case:
( - 1 / 27 )^⅔ = √ [ ( - 1 / 27)^3 ]
Square root of negative number us complex number, so the solution is:
x = 1 / 27
Solve for x if x^-⅔=9
2 answers
but
(-1/27)^(2/3)
= [(-1/27)^(1/3)]^2
= (-1/3)^2
= 1/9
both answers verify
x = ± 1/27
(-1/27)^(2/3)
= [(-1/27)^(1/3)]^2
= (-1/3)^2
= 1/9
both answers verify
x = ± 1/27