Question 196586
Is the equation *[Tex \LARGE x^{\frac{3}{2}}=27] ???



*[Tex \LARGE x^{\frac{3}{2}}=27] ... Start with the given equation.



*[Tex \LARGE \sqrt[3]{x^{\frac{3}{2}}}=\sqrt[3]{27}] ... Take the cube root of both sides



*[Tex \LARGE x^{\frac{1}{2}}=\sqrt[3]{27}] ... Take the cube root of *[Tex \LARGE x^{\frac{3}{2}}] to get *[Tex \LARGE x^{\frac{1}{2}}]



*[Tex \LARGE x^{\frac{1}{2}}=3] ... Take the cube root of 27 to get 3



*[Tex \LARGE \left(x^{\frac{1}{2}}\right)^2=(3)^2] ... Square both sides



*[Tex \LARGE x=(3)^2] ... Square *[Tex \LARGE x^{\frac{1}{2}}] to get "x"



*[Tex \LARGE x=9] ... Square 3 to get 9



So the solution is *[Tex \LARGE x=9]