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.

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7 Answers

Anonymous 0 Comments

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).

Anonymous 0 Comments

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.

Anonymous 0 Comments

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).

Anonymous 0 Comments

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.

Anonymous 0 Comments

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”.

Anonymous 0 Comments

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.

Anonymous 0 Comments

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>