Question 1010835
In how many different ways can a true-false test consisting 
of 9 questions be answered?
<pre><font size=1><b>
There are 2 ways to answer question 1.

For each of those 2 ways to answer question 1, 
there are 2 ways to answer question 2.
That's 2*2 or 2<sup>2</sup> ways to answer questions 1 and 2.

For each of those 2<sup>2</sup> ways to answer questions 1 and 2, 
there are 2 ways to answer question 3.
That's 2*2*2 or 2<sup>3</sup> ways to answer questions 1 through 3.

For each of those 2<sup>3</sup> ways to answer questions 1 through 3, 
there are 2 ways to answer question 4.
That's 2*2*2*2 or 2<sup>4</sup> ways to answer questions 1 through 4.

For each of those 2<sup>4</sup> ways to answer questions 1 through 4, 
there are 2 ways to answer question 5.
That's 2*2*2*2*2 or 2<sup>5</sup> ways to answer questions 1 through 5.

For each of those 2<sup>5</sup> ways to answer questions 1 through 5, 
there are 2 ways to answer question 6.
That's 2*2*2*2*2*2 or 2<sup>6</sup> ways to answer questions 1 through 6.

For each of those 2<sup>6</sup> ways to answer questions 1 through 6, 
there are 2 ways to answer question 7.
That's 2*2*2*2*2*2*2 or 2<sup>7</sup> ways to answer questions 1 through 7.

For each of those 2<sup>7</sup> ways to answer questions 1 through 7, 
there are 2 ways to answer question 8.
That's 2*2*2*2*2*2*2*2 or 2<sup>8</sup> ways to answer questions 1 through 8.

For each of those 2<sup>8</sup> ways to answer questions 1 through 8, 
there are 2 ways to answer question 9.
That's 2*2*2*2*2*2*2*2*2 or 2<sup>9</sup> ways to answer questions 1 through 9.

Answer: 2<sup>9</sup> = 512 ways.

Edwin</pre></font></b>