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Multiplication and Division of Terms Study Guide (page 3)

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Updated on Oct 3, 2011

Example

(18a4b3) ÷ (–6ab5) =

Begin with the coefficients: 18 ÷ –6 = –3.

Carry the bases of the dividend into the answer. The answer has bases of a and b.

There are no bases in the dividend that are not in the divisor, and vice versa, so we are ready to subtract.

The exponent of a in the dividend is 4 and the exponent of a in the divisor is 1: 4 –1 = 3. The exponent of a in the answer is 3. The exponent of b in the dividend is 3 and the exponent of b in the divisor is 5. 3 –5 = –2. The exponent of b in the answer is –2.

Put it all together: (18a4b3) ÷ (–6ab5) = –3a3b–2. It is okay to have a negative exponent in your answer! If you would like to avoid negative exponents, this answer can also be written as.

Example

(16c7) ÷ (4c7) =

Begin again with the coefficients: 16 ÷ 4 = 4.

There is only one base in the dividend and the divisor, c. Subtract the exponent of c in the dividend from the exponent of c in the denominator: 7 – 7 = 0. What does this mean? We could write our answer as 4c°, but because any number or variable to the power of 0 is equal to 1, c° = 1 and 4(1) = 4. In other words, if the exponent of a base is the same in both the dividend and the divisor, that base does not appear in your answer.

Tip:

If the coefficient of the dividend and the divisor are the same, your answer does not appear to have a coefficient. That is because any value divided by itself is equal to 1, and it is unnecessary to write the number 1 as the coefficient of a term.

Find practice problems and solutions for these concepts at Multiplication and Division of Terms Practice Questions.

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