Chapter 4.3, Problem 44IP

To determine

To find: that how many times as great is the length of the large beetle than the length of the small beetle.

Answer to Problem 44IP

The length of the large beetle than the length of the small beetle is $2^9$ times greater.

Explanation of Solution

Given information:

Length of large beetle is $2^7$ millimeter and small beetle length is $2^{-2}$ millimeter.

Calculation : to find that how many times as great is the length of the large beetle than the length of the small beetle, compare the length of the larger beetle and small beetle.

Let the length of large beetle is x time greater as a length of small beetle,

  $\begin{array}{l}\text{lenght of large beetle}=x·\text{length of small beetle}\\ 2^7=x·2^{-2}\text{ [substitute]}\\ x=\frac{2^7}{2^{-2}}\text{ [divide]}\\ x=2^{7-\left(-2\right)}\text{ [}{a}^m÷a^n=a^{m-n}]\\ x=2^9\text{ [simplify the exponents]}\end{array}$

Thus, The length of the large beetle than the length of the small beetle is $2^9$ times greater.