Arithmetic of Computers

Arithmetic of Computers

from Tenscope Limited

Lesson 2

The Arithmetic of Powers

Multiplication by addition, and division by subtraction

Page 85

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Your answer :
(43)/(41) = 16
You are correct. Now, we have just shown that we can write the result of the division 43 by 41 in two ways:
As a power of 4: (43)/(41)  = 4(3 − 1) = 42; Or as a regular number: (43)/(41)  = (64)/(4) = 16.
Since (43)/(41) = 42 and also  = 16, it follows that 42 = 16, which is no surprise to anyone. From this we can conclude that our two methods of solving a problem in division of powers of numbers give us the same, or equal, results.
Now let’s apply our division rule
(bm)/(bn) = b(m − n)
to the problem of dividing a power of a number by itself. let’s take the case of divising 43 by 43.
(43)/(43) = ?
By our division rule, what result will we get from this division, if we write the result as some power of 4?
Answer :
(43)/(43) = 4(3 − 3) = 40.

Go to Page 61

(43)/(43) = (64)/(64) = 1.

Go to Page 81


Answer to Self-Test Question 16, Lesson 2 :
33; 27.

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