Chapter 3.3, Problem 3QR

To determine

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

Answer to Problem 3QR

The required expression is $3x^2-2x^{-1}+5x^{-2}$ .

Explanation of Solution

Given information:

The expression $=3x^2-\frac{2}{x}+\frac{5}{x^2}$

Formula used:

Property of negative exponent:

  $\frac{1}{x^n}=x^{-n}$

Calculation:

The given expression is $3x^2-\frac{2}{x}+\frac{5}{x^2}$ .

To write the above expression as a sum of powers of x , use the property of negative exponent.

  $3x^2-\frac{2}{x}+\frac{5}{x^2}=3x^2-2x^{-1}+5x^{-2}$

Hence, the required expression is $3x^2-2x^{-1}+5x^{-2}$ .