[0/1 Points] DETAILS MY NOTES HARMATHAP11 0:4.060. 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 in this form. $$ \frac{-4}{3 \sqrt[6]{x^{5}}} $$ $$ -436 x^{-5} $$ SUBMIT ANSWER

Question

UpStudy AI · Accepted Answer

To express each of the given expressions in the form $$ c x^{n} $$, where $$ c $$ is a constant and $$ n $$ is a rational number, follow these steps:

1. **First Expression:**
   
   $$
   \frac{-4}{3 \sqrt[6]{x^{5}}}
   $$
   
   - Rewrite the sixth root as an exponent:
     
     $$
     \sqrt[6]{x^{5}} = x^{5/6}
     $$
   
   - Substitute back into the expression:
     
     $$
     \frac{-4}{3 x^{5/6}} = -\frac{4}{3} \cdot x^{-5/6}
     $$
   
   So, the first expression in the form $$ c x^{n} $$ is:
   
   $$
   -\frac{4}{3} x^{-5/6}
   $$

2. **Second Expression:**
   
   $$
   -436 x^{-5}
   $$
   
   This expression is already in the desired form $$ c x^{n} $$, where:
   
   - $$ c = -436 $$
   - $$ n = -5 $$
   
   So, no further modification is needed.

**Final Answer:**
$$
\frac{-4}{3 \sqrt[6]{x^{5}}} = -\frac{4}{3} x^{-5/6}
$$
$$
-436 x^{-5} \quad \text{(already in the form } c x^{n}\text{)}
$$
The expression $$ \frac{-4}{3 \sqrt[6]{x^{5}}} $$ can be written as $$ -\frac{4}{3} x^{-5/6} $$. The second expression $$ -436 x^{-5} $$ is already in the form $$ c x^{n} $$.

Solución de tutoría real

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Calculus Questions