Chapter 7.3, Problem 60PPE

To determine

To simplify: The expression ${\left({10}^3\right)}^4\left(4.3\times {10}^{-8}\right)$ .

Answer to Problem 60PPE

The required answer is $4.3\times {10}^4$ .

Explanation of Solution

Given information:

The given expression ${\left({10}^3\right)}^4\left(4.3\times {10}^{-8}\right)$ .

Calculation:

  $\begin{array}{l}={\left({10}^3\right)}^4\left(4.3\times {10}^{-8}\right)\\ ={10}^{12}\cdot 4.3\cdot {10}^{-8}\end{array}$

(Multiply exponents when raising a power to a power)

  $={10}^{12}\cdot {10}^{-8}\cdot 4.3$

(Commutative property of multiplication)

  $={10}^{12+\left(-8\right)}\cdot 4.3$

(Add exponents when multiplying powers with the same base)

  $\begin{array}{l}={10}^4\cdot 4.3\\ =43000\\ =4.3\times {10}^4\end{array}$

(Simplify)