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. Write the following expression \( \frac{-8}{7 \sqrt[6]{x^{5}}} \) [-/1 Points] DETAILS MY NOTES HARMATHAP12 9.4.011.

To rewrite the expression \( \frac{-8}{7 \sqrt[6]{x^{5}}} \), we can express the square root as a fractional exponent. The sixth root of \( x^{5} \) can be written as \( x^{5/6} \). Thus, we have: \[ \frac{-8}{7} \cdot \frac{1}{x^{5/6}} = \frac{-8}{7} x^{-5/6} \] So the final expression is: \[ \frac{-8}{7} x^{-5/6} \] --- Imagine you’re at a math party, and someone drops the equivalent of a math bomb: a complicated fraction! To tackle it, you just need to remember that any root can be converted to an exponent. This nifty trick transforms messy fractions into something more manageable, keeping the party fun and the math flowing! When you encounter expressions like this in calculus, don't shy away! These transformations allow you to simplify expressions, making it easier to apply rules like differentiation or integration later on. The clearer your expression, the smoother your math journey!