Math CentralQuandaries & Queries


Question from jessie, a student:

Can you please explain how to put x^3 y^2 times x^1 y^3 in simplest exponential form?

Hi Jessie,

Let me try a3 b1 times a2 b5. You can write this as

a3 b1 × a2 b5 = (a × a × a) × b × (a × a) × (b × b × b × b × b)

What I have now is five a's and six b's and I can write this as

a3 b1 × a2 b5 = (a × a × a × a × a) × (b × b × b × b × b × b) = a5 b6.


a3 b1 × a2 b5 = a5 b6.

Notice that what I did was collect the three a's from a3 with the two a's from a2 to get five a's. In other words

a3 × a2 = a3+2 = a5


b1 × b5 = b1+5 = b6

so all I need to do is add the exponents.

Let's try another,

p5 q2 × p2 q3 = p5+2 q 2+3 = p7 q5

I hope this helps,

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