Answer
$x=±\sqrt {14}$
Work Step by Step
$(x^2-5)^{\frac{3}{2}}=27~~$ (Square both sides)
$[(x^2-5)^{\frac{3}{2}}]^2=27^2$
$(x^2-5)^3=729$
$x^2-5=\sqrt[3] {729}$
$x^2-5=9$
$x^2=14$
$x=±\sqrt {14}$
Check the solutions:
$x=\sqrt {14}$
$[(\sqrt {14})^2-5]^{\frac{3}{2}}=(14-5)^{\frac{3}{2}}=9^{\frac{3}{2}}=(\sqrt 9)^3=3^3=27$
$x=-\sqrt {14}$
$[(-\sqrt {14})^2-5]^{\frac{3}{2}}=(14-5)^{\frac{3}{2}}=9^{\frac{3}{2}}=(\sqrt 9)^3=3^3=27$
