Chapter 3.3, Problem 6QR

To determine

The expression by writing it as a sum of powers of x .

Answer to Problem 6QR

The required expression is $x^2+x$ .

Explanation of Solution

Given information:

The expression $=\frac{x^{-1}+x^{-2}}{x^{-3}}$

Formula used:

Property of quotient of like bases:

  $\frac{a^m}{a^n}=a^{m-n}$

Calculation:

The given expression is $\frac{x^{-1}+x^{-2}}{x^{-3}}$ .

To write the above expression as a sum of powers of x , use property of quotient of like bases.

  $\begin{array}{c}\frac{x^{-1}+x^{-2}}{x^{-3}}=\frac{x^{-1}}{x^{-3}}+\frac{x^{-2}}{x^{-3}}\\ =x^{-1-\left(-3\right)}+x^{-2-\left(-3\right)}\\ =x^{-1+3}+x^{-2+3}\\ =x^2+x\end{array}$

Hence, the required expression is $x^2+x$ .