To divide exponents (or powers) with the same base, subtract the exponents. Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base. Learn about exponents, examples of exponents and methods of division with exponents using the resources on this page.

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The terms 32 and 33 both have 3 as the base number, so they are said to have like bases. This can be written as 27. The 7 came from adding the exponents: 4 + 3. When you multiply terms with like bases you add the exponents together.

Here you can use the rules for multiplying and dividing powers. Remember these rules: To multiply powers you add, eg, 105 × 103 = 10. To divide powers you subtract, eg, 105 ÷ 103 = 10.

So each time you perform an operation on fractions and your answer ends up as an improper fraction, you will usually need to simplify your answer. The results will be in the form of a mixed number. So to convert an improper fraction into a mixed number, we just divide the numerator by the denominator.

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, “x–2” (ecks to the minus two) just means “x2, but underneath, as in 1/(x2)”.