Simplify the expression.

Question

Simplify the following expressions using fractional exponents, I forgot how to do this type, do I rationalize it? or can it just cancel each other out?

$ {\Large \frac{\sqrt[ 5 ]{x^{ 3 }}}{ \sqrt{x} } = }$ ?

Cheers

Answer 1

$$\frac{\sqrt[5]{x^3}}{\sqrt{x}}=\frac{x^{3/5}}{x^{1/2}}=\frac{x^{3/5}}{x^{1/2}}\times\frac{{\color{red}{x^{2/5}}}\times\color{blue}{x^{1/2}}}{{\color{red}{x^{2/5}}}\times\color{blue}{x^{1/2}}}=\frac{x^{3/5}\times\color{red}{x^{2/5}} }{x^{1/2}\times\color{blue}{x^{1/2}}}\times\frac{\color{blue}{x^{1/2}}}{\color{red}{x^{2/5}}}=\frac{x}{x}\times x^{1/2-2/5}=x^{1/10},~~x\neq0$$

Answer 2

$$\frac{\sqrt[5]{x^3}}{\sqrt{x}}=x^{\frac 35 -\frac 12}=x^{\frac{1}{10}}=\sqrt[10]{x}. $$

Michael