Math CentralQuandaries & Queries


Question from Tanisha, a student:

I would just like to double check if something like 5x squared times 4x cubed equals 20x to the power of 5??
It's just that we were told you can only answer an equation like this if the base is the does that mean the x part or the whole thing like 5x?
I'm sorry if that didn't make sense!

Thank you for your help!!

Hi Tanisha,

Your question makes perfectly good sense. To avoid this type of confusion mathematicians have developed conventions in the writing of mathematical expressions. One of these conventions or rules is that powers are performed before multiplication. For example the expression $7 \times 3^2$ is evaluated by

\[7 \times 3^2 = 7 \times 9 = 63.\]

If you want to square both the 7 and the 3 you would need to write $(7 \times 3)^2$ since one of the conventions concerning order of operations is that you perform whatever is inside parentheses or brackets first. Thus

\[(7 \times 3 )^2 = (21)^2 = 441.\]

In your expressions $5x^2$ and $4x^3$ there is an implied multiplication between the $5$ and the $x^2$ and also between the $4$ and the $x^3$ and hence

\[5x^2 \times 4x^3 = 5 \times x^2 \times 4 \times x^3\]

and since multiplication is commutative

\[5x^2 \times 4x^3 = 5 \times x^2 \times 4 \times x^3 = 5 \times 4 \times x^2 \times x^3 = 20 \times x^5 = 20x^5\]

I hope this helps,

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