## Elementary Algebra

$\dfrac{4\sqrt{x}}{x^4}$
Using the properties of radicals, the given expression, $\dfrac{4}{\sqrt{x^7}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4}{\sqrt{x^7}}\cdot\dfrac{\sqrt{x}}{\sqrt{x}} \\\\= \dfrac{4\sqrt{x}}{\sqrt{x^8}} \\\\= \dfrac{4\sqrt{x}}{\sqrt{(x^4)^2}} \\\\= \dfrac{4\sqrt{x}}{x^4} .\end{array} Note that all variables are assumed to represent positive real numbers.