# How Do Exponents Work

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Okay so let’s say, hypothetically, I have the equation FL^3. Does it turn into F^3 times L^3, or F times L^3, or (F times L)^3. Literally no one has ever explained this to me and I’ve always just been too afraid to ask and now i’m taking engineering and I’m very confused. I’ve tried googling it but nothing has given me a straight answer. Please help.

In: 3 It’s generally assumed that FL is FxL, so FL^3 is FxL^(3). According to pemdas you do the exponent before the multiplication. If the F was cubed it would be F^(3)L^(3). So assuming that F and L are individual variables there, FL^3 = F times L times L times L, so F times L^3.

If you had (FL)^3, that would be F^3 times L^3. The parentheses matter. FL^3 becomes F * L^3 .

The exponent is a little special in that it only applies to whatever it’s immediately next to. There’s always a hidden `*` when you write formulae like AB^2 , so there’s never any ambiguity. If the writer intends FL^(3)=F^(3)*L^(3), they really should have written (FL)^(3) . It may be useful to convince yourself that (FL)^(3) indeed equals F^(3)L^(3). Otherwise, you should read FL^(3)=F*L^(3). Disclaimer: I’m not a mathematician, but it seems to me that “FL3” is poor formatting, or bad syntax. If you’re writing down the equation, you’re communicating how the numbers are meant to work together. So better syntaxes would be either (FL)3, or FxL3, depending on what you’re trying communicate.

It’s kinda like the Oxford comma for maths. PEMDAS: Parentheses, Exponentiation, Multiplication, Division, Addition, Subtraction. This is the order of operations. Exponentiation comes before multiplication. So in FL^3, we apply the exponent 3 to L before doing the multiplication with F. Thus it’s “F * L^3”. The following explanation assumes whoever wrote the equation knew what they were doing.

When multiplying variables there is an implied * between any letters. AB=A*B.

Therefore FL<sup>3</sup> =F*L<sup>3.</sup>

If the author intends for this to equal F<sup>3</sup>*L<sup>3,</sup> they would write it out as (FL)<sup>3.</sup>

Because the implied * is standardized in mathematics notation, if the parentheses are not there it is safe to assume the equation was meant to read as F*L<sup>3.</sup>