Solve the Equation Including a Variable Raised to a Rational Exponent

Solve the equation in which a variable is raised to a rational exponent: $x^{\frac{5}{4}} = 32.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The way to remove the exponent on x is by raising both sides of the equation to a power that is the reciprocal of $\frac{5}{4},$ which is $\frac{4}{5} .$

$\begin{matrix} x^{\frac{5}{4}} & = & 32 \\ {(x^{\frac{5}{4}})}^{\frac{4}{5}} & = & {(32)}^{\frac{4}{5}} \\ x & = & {(2)}^{4} & The fifth root of 32 is 2. \\ = & 16 \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the equation $x^{\frac{3}{2}} = 125.$

How did it go?