In calculus it is frequently important to write an expression in the form \( c x^{n} \), where \( c \) is a constant and \( n \) is a rational number \( \frac{-8}{5 \sqrt[4]{x^{3}}} \)

To rewrite the expression \( \frac{-8}{5 \sqrt[4]{x^{3}}} \) in the form \( c x^{n} \), we start by converting the denominator into a form involving a power of \( x \). The fourth root of \( x^3 \) can be expressed as \( x^{3/4} \). Thus, the given expression can be rewritten as \( \frac{-8}{5} \cdot x^{-3/4} \) or simply \( -\frac{8}{5} x^{-3/4} \). Now it is in the desired form where \( c = -\frac{8}{5} \) and \( n = -\frac{3}{4} \). This transformation is particularly useful when applying calculus concepts like differentiation and integration, as it simplifies the manipulation of the terms. To find the derivative, for example, we can easily apply the power rule. The more you practice expressing equations this way, the more intuitive it becomes to switch between forms and apply calculus techniques seamlessly!