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Help w Maths🙃

T to the power 3= mn/m-n

M=4x10 to the power 12
N=3x10 to the power 9

Work out T.

Eh I multiplied m and n together (to get MN) and got 12x10 to the power 21 (I know you can't have numbers above 12 in standard form but I have no idea whether what I'm doing is correct).

Then I did m-n and got 1x10 to the power 3.

Did the division sum= 12x10 to the power 21 divided by 1x10 to the power 3 and got 12x10 to the power 18=1.2x10 to the power 19.

T to the power 3= 1.2x10 to the power 19.

'Cube rooted' it and the answer I got for T was 2289428.485.

It wants the answer in standard form to 3 significant figures= 2.29x10 the power 6.

Is this completely wrong or? Probably just over complicated a really simple question but help would be appreciated:smile:
Original post by idfk_
X


Your first step (m x n) is correct. However, 4×1012−3×1094\times 10^{12} - 3\times 10^9 is not 1×1031\times 10^3. Adding and subtracting gets a bit more complicated if the tens are to different powers (you do not subtract the exponents if you're just doing subtraction) so if you're not using a calculator, you need to manually put them to the same power. 3×109=0.003×10123\times 10^9 = 0.003\times 10^12 so m−n=4×1012−0.003×1012=3.997×1012m - n = 4\times 10^{12} - 0.003\times 10^{12} = 3.997 \times 10^{12}.
Reply 2
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idfk_
OP
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Original post by Plagioclase
Your first step (m x n) is correct. However, 4×1012−3×1094\times 10^{12} - 3\times 10^9 is not 1×1031\times 10^3. Adding and subtracting gets a bit more complicated if the tens are to different powers (you do not subtract the exponents if you're just doing subtraction) so if you're not using a calculator, you need to manually put them to the same power. 3×109=0.003×10123\times 10^9 = 0.003\times 10^12 so m−n=4×1012−0.003×1012=3.997×1012m - n = 4\times 10^{12} - 0.003\times 10^{12} = 3.997 \times 10^{12}.


Thankyou!!

So, would I go about it the same way when I do the division and then cube root the answer to get to T?
Original post by idfk_
Thankyou!!

So, would I go about it the same way when I do the division and then cube root the answer to get to T?


So you now know what mnmn and m−nm-n are (12×1021=1.2×1022 12 \times 10^{21} = 1.2 \times 10^{22} and 3.997×1012 3.997\times 10^{12} respectively) so yes, you just do a simple division. You will probably want to do this on your calculator though, unless you're particularly keen on working out what 1.23.997\frac{1.2}{3.997} is by hand!
Reply 4
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idfk_
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Original post by Plagioclase
So you now know what mnmn and m−nm-n are (12×1021=1.2×1022 12 \times 10^{21} = 1.2 \times 10^{22} and 3.997×1012 3.997\times 10^{12} respectively) so yes, you just do a simple division. You will probably want to do this on your calculator though, unless you're particularly keen on working out what 1.23.997\frac{1.2}{3.997} is by hand!


Calculator it is.

From that I get the answer 3002251689. Cube root it to get T=1442.610313

Which is equal to 1.44x10 to the power 3?
Original post by idfk_
Calculator it is.

From that I get the answer 3002251689. Cube root it to get T=1442.610313

Which is equal to 1.44x10 to the power 3?


Yep, that's what I've got! :yep:
Reply 6
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idfk_
OP
11
Original post by Plagioclase
Yep, that's what I've got! :yep:


Again, thanks a lot! Wouldn't have got to that myself:smile:

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