Arithmetic of Computers

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Lesson 2

The Arithmetic of Powers

Multiplication by addition, and division by subtraction

Page 62

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Your answer :

(4²)(4¹) = 4³.

You are correct. (4²)(4¹) = 4^(2 + 1) = 4³,

Now, you can reach this result by using our rule that

(b^m)(bⁿ) = b^(m + n)

where b = 4, m = 2 and n = 1. You can see that our rule is reasonable since

(4²) = 4 × 4, (4¹) = 4.

Therefore, (4²)(4¹) = (4 × 4) × 4 = (4 × 4 × 4) = 4³ = 4^(2 + 1).

The total number of times the base is used as a factor in the product is simply the total number of times it is used as a factor in the two numbers that are to be multiplied. The exponents of the two numbers that are to be multiplied give the number of times the base is used as a factor in each number. The sum of the exponents, therefore, gives the total number of times the base is used as a factor in the product.

What is the product of (7²)(7³)?

Answer :

(7²)(7³) = 7⁵.