Chapter 4.1, Problem 25IP

a.

To determine

Find how long is the chain of volcanoes.

Answer to Problem 25IP

The chain of volcanoes is $30,000$ miles long.

Explanation of Solution

Calculation:

From the given,

  ${10}^4$ is the multiplication of a series of four 10s.

  $\begin{array}{l}{10}^4=\mathrm{10.10.10.10}\\ =10,000\text{ Multiply}\end{array}$

Therefore,

  $\begin{array}{l}{3.10}^4\\ =\mathrm{3.10.10.10.10}\\ =3.10,000\text{ Multiply}\\ =30,000\text{ Simplify}\end{array}$

Thus the chain of volcanoes is $30,000$ miles long.

b.

To determine

Find the chain of volcanoes.

Answer to Problem 25IP

There are $1,215$ volcanoes

Explanation of Solution

Calculation:

From the given,

  $3^5$ is the multiplication of a series of five 3s.

  $\begin{array}{l}{3}^5=3\cdot 3\cdot 3\cdot 3\cdot 3\\ =243\text{ Multiply}\end{array}$

Therefore,

  $\begin{array}{l}{3}^5\cdot 5=243.5\text{ Multiply}\\ =1,215\end{array}$

Thus there are $1,215$ volcanoes