Chapter 4.1, Problem 35OE

To determine

To explain: The first figure is written as “ b squared” and second as “ b cubed”.

Answer to Problem 35OE

In first figure b as a base is used twice and in second figure it is used thrice.

Explanation of Solution

Given information:

The figures are provided below,

Formula used:

The expression of the form $a^n$ is expressed as $a\cdot a\cdot a\cdot \dots \cdot a\left[n\text{ times}\right]$ where a is the base and n is the exponent.

Calculation:

Consider the figures that are provided below,

The area of square of side sis $s^2$ .

In the first figure the side of square is b .

Therefore, area of square is $b^2$ .

Recall that the expression of the form $a^n$ is expressed as $a\cdot a\cdot a\cdot \dots \cdot a\left[n\text{ times}\right]$ where a is the base and n is the exponent.

Compare $b^2$ and $a^n$ . Here a is $b$ and n is 2.

So, $b$ as a base 2 times or it can be read as b squared.

  $b^2=b\cdot b$

Next, the volume of cube of side sis $s^3$ .

In the second figure the side of cube is b .

Therefore, volume of cube is $b^3$ .

Recall that the expression of the form $a^n$ is expressed as $a\cdot a\cdot a\cdot \dots \cdot a\left[n\text{ times}\right]$ where a is the base and n is the exponent.

Compare $b^3$ and $a^n$ . Here a is $b$ and n is 3.

So, $b$ as a base 3 times or it can be read as b cubed.

  $b^3=b\cdot b\cdot b$

Thus, in first figure b as a base is used twice and in second figure it is used thrice.