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Nairaland Forum / Science/Technology / Programming / Anoda Law Of Indices? (970 Views)
Anoda Law Of Indices? by asalimpo(m): 5:31am On Oct 01, 2017 |
Is this a valid law of indices? a^(b*c) = (a^b)^c. = a^(b^c) = a^(c*b). plug in any number for a,b or c. Discovered by mistake when thinking on a problem. if it's a law, why were'nt we so taught in school? Secondary school though. huh!! We were taught +,-,division, why not multiplication? |
Re: Anoda Law Of Indices? by bolkay47(m): 8:31am On Oct 01, 2017 |
asalimpo:I guess you are referring to the power rule. p^m(n)=p^mn etc. The power rule exists and has always been taught. 1 Like |
Re: Anoda Law Of Indices? by asalimpo(m): 9:29am On Oct 01, 2017 |
I dont understand you: but if this is what you mean - 2^3(4)= (8(4))=32 That's not what i mean. i mean: 5^(6*7) = (5^6)^7 = 5^6^7 =5^7^6 the * is translated to ^. notice that? notice how order doesnt matter for the numbers in the brackets just like it works for normal *. e.g a*b = b*a, 5^(6*7) = 5^(7*6). Interesting. This old stuffs nothing new. mathematicians know it, just discovered it and wondered why it's not it maths books and not in the typical laws of indices were were taught in school. There's a law that works for multiplication like there is for addition a^(b+c) = a^b * a^c , subtraction, etc. |
Re: Anoda Law Of Indices? by bolkay47(m): 1:44pm On Oct 01, 2017 |
asalimpo:p^m(n)=p^(mn). 2^2(5)=2^10. |
Re: Anoda Law Of Indices? by bolkay47(m): 1:57pm On Oct 01, 2017 |
For a^b^c. Consider: 2^2^2=2^(2^2)=2^4=16. CHECK THIS OUT (2^2)^2=4^2=16. CHECK 3^3^3=3^(3^3)=3^27. 3^3^3=3^3(^3)=27^3. Therefore 3^27=27^3. I applied the power rule just that this kind of problem require you to simplify the powers. I agree with the fact that authors tend to overlook it. ....except in further or complex mathematics. |
Re: Anoda Law Of Indices? by asalimpo(m): 2:08pm On Oct 01, 2017 |
bolkay47:You're right. I thought i had discovered something new!! miscontrued the syntax. 2^nb = 2^(n*b) = 2^n^b. correction: 3^27 != 27^3. I've been so used to computer syntax, the math connotation isnt obvious. a^bc is a^(b*c). It's an old known law. |
Re: Anoda Law Of Indices? by bolkay47(m): 3:34pm On Oct 01, 2017 |
asalimpo:Sorry, I wanted to type the not equal sign. I wanted to illustrate the bottleneck using those examples. |
Re: Anoda Law Of Indices? by bolkay47(m): 3:35pm On Oct 01, 2017 |
asalimpo:It's alright sir! |
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