In calculus, it is frequently important to write an expression in the form , where c is a constant and n is a rational number. Write the expression in this form.

Question

Quizplus · Accepted Answer

We can write the expression as $\frac{3}{\sqrt[3]{x}}+\frac{11}{\sqrt[3]{x^2}}$. Now, $\sqrt[3]{x}=x^{\frac{1}{3}}$, so we can use laws of exponents to write $\frac{3}{\sqrt[3]{x}}=3x^{-\frac{1}{3}}$. Similarly, $\sqrt[3]{x^2}=x^{\frac{2}{3}}$, so $\frac{11}{\sqrt[3]{x^2}}=11x^{-\frac{2}{3}}$. Thus, we have written the expression in the form $c_1x^{n_1}+c_2x^{n_2}$, where $c_1=3$, $n_1=-\frac{1}{3}$, $c_2=11$, and $n_2=-\frac{2}{3}$. The only answer choice that matches these values is $\boxed{	extbf{(C)}}$.

In Calculus, It Is Frequently Important to Write an Expression