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Lesson 2
The Arithmetic of Powers
Multiplication by addition, and division by subtraction
You are correct. A division is often indicated in fractional form, as shown below, and we may therefore call the number 24 in our example the dividend.
dividend →
divisor →
(24)/(4) = 6 ← quotient
We may now state the rule for division of one power of a number by another power of the same number. Expressed in symbols the rule is
(bm)/(bn) = b(m − n)
and in words: When one power of a base is divided by another power of the same base, the exponent of the quotient is the difference between the exponent of the dividend and the exponent of the divisor. To state the rule loosely, you subtract exponents to divide just as you add exponents to multiply.
