Chapter 1.1, Problem 37PPS

(a)

To determine

Find the missing values in the table.

  

Answer to Problem 37PPS

${10}^2$	$\times$	${10}^3$	=	$10\times 10\times 10\times 10\times 10$	=	${10}^5$
${10}^2$	$\times$	${10}^4$	=	$10\times 10\times 10\times 10\times 10\times 10$	=	${10}^6$

Explanation of Solution

In the table it is clearly shown that number of power is the number of times multiplied to itself.

Power of $10$ is increasing in the second row while the power of the first row remains constant. On multiplying the $10$ number of times as its power is written.

The answer is as ${10}^{5}and{10}^6$ for two respective rows.

(b)

To determine

  

Make an equation satisfying the table.

Answer to Problem 37PPS

  ${10}^2\times {10}^n={10}^{2+n}$ , where $n$ is an integer.

Explanation of Solution

First two rows shows the pattern of addition of the power of $10$ .

In the third row, total number of $10$ multiplied by itself is given.

Add the total number of $10$ and writes it in power form over base $10$ .

The required solution will be ${10}^2\times {10}^n={10}^{2+n}$ for the above mentioned table.

(c)

To determine

  

Formulate conjecture about exponent of the product of two powers with like bases.

Answer to Problem 37PPS

The powers add up as discussed below.

  ${10}^m\times {10}^n={10}^{m+n}$

Explanation of Solution

Table shows an example of the addition of power of the same base when multiplied together.

When two term of same base multiplied by each other, then base remains the same and power get added up to the same base.

  ${10}^m\times {10}^n={10}^{m+n}$ , where $mandn$ are any integer.