Question

write the expression shown below in radical form.
$x^{-\frac{9}{8}}$
$x^{-\frac{9}{8}} = \square$
(simplify your answer, including any radicals. use integers or exponents only.)

Explanation:

Step1: Handle negative exponent

$x^{-\frac{9}{8}} = \frac{1}{x^{\frac{9}{8}}}$

Step2: Split the rational exponent

$\frac{1}{x^{\frac{9}{8}}} = \frac{1}{x^{1+\frac{1}{8}}} = \frac{1}{x \cdot x^{\frac{1}{8}}}$

Step3: Convert to radical form

$\frac{1}{x \cdot x^{\frac{1}{8}}} = \frac{1}{x\sqrt[8]{x}}$

Answer:

$\frac{1}{x\sqrt[8]{x}}$