Chapter 7.3, Problem 58PPE

To determine

To simplify: The expression ${\left(2x^{-3}\right)}^2{\left(0.2x\right)}^2$ .

Answer to Problem 58PPE

The required answer is $0.16x^{-4}$ .

Explanation of Solution

Given information:

The given expression ${\left(2x^{-3}\right)}^2{\left(0.2x\right)}^2$ .

Calculation:

  $\begin{array}{l}={\left(2x^{-3}\right)}^2{\left(0.2x\right)}^2\\ =2^2{\left(x^{-3}\right)}^2{\left(0.2\right)}^2{x}^2\end{array}$

(Raise each factor to the second power)

  $=2^2\cdot x^{-6}\cdot {0.2}^2\cdot x^2$

(Multiply exponents when raising a power to a power)

  $=2^2\cdot {0.2}^2\cdot x^{-6}{x}^2$

(Commutative property of multiplication)

  $=4\cdot 0.04\cdot x^{-6+2}$

(Add the exponents of powers with the same base)

  $=0.16x^{-4}$

(Simplify)