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Quick q about cancelling fractions?

Q. (g-7)^9 / (g-7)^3. I know the answer is (g-7)^6 but why wouldn't I be able to cancel both the (g-7)'s?

If I get any question such as this should I refrain from cancelling two same things in the numerator and denominator as it'll leave the power on its own?
Reply 1
Avatar for elisabethr
elisabethr
Okay, you're kinda right, but it'a a power, not a multiplier
ie, 2(g-7) is different from (g-7)^2

Think of it as
(g-7)(g-7)(g-7)(g-7)(g-7)(g-7)(g-7)(g-7)(g-7)
-----------------------------------------------------
(g-7)(g-7)(g-7)

now cancel :smile:
Reply 2
Avatar for iSoftie
iSoftie
14
Do you know your indices rules?
Original post by Magenta96
Q. (g-7)^9 / (g-7)^3. I know the answer is (g-7)^6 but why wouldn't I be able to cancel both the (g-7)'s?

If I get any question such as this should I refrain from cancelling two same things in the numerator and denominator as it'll leave the power on its own?


(g-7)^9 is (g-7)(g-7)(g-7)(g-7)(g-7)(g-7)(g-7)(g-7)(g-7) and (g-7)^3 is (g-7)(g-7)(g-7) therefore you are effectively cancelling g-7 from top and bottom, but you can only cancel 3 from top and bottom, leaving you with (g-7)^6
Reply 4
Avatar for raheem94
raheem94
13
Original post by Magenta96
Q. (g-7)^9 / (g-7)^3. I know the answer is (g-7)^6 but why wouldn't I be able to cancel both the (g-7)'s?

If I get any question such as this should I refrain from cancelling two same things in the numerator and denominator as it'll leave the power on its own?


(g−7)9(g−7)3=(g−7)9(g−7)−3=(g−7)9−3=(g−7)6 \dfrac{(g-7)^9}{(g-7)^3} = (g-7)^9(g-7)^{-3} = (g-7)^{9-3} = (g-7)^{6}
Reply 5
Avatar for Magenta96
Magenta96
OP
16
ohh thanks, I guess I was getting muddled up with subtracting indices and cancelling the same thing on algebraic fractions on the top and bottom. Thanks I understand a lot better now, :smile:

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