₦airaland Forum

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?

asalimpo:
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?

I guess you are referring to the power rule. p^m(n)=p^mn etc. The power rule exists and has always been taught.

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.

asalimpo:
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.

p^m(n)=p^(mn). 2^2(5)=2^10.

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.

bolkay47:
p^m(n)=p^(mn). 2^2(5)=2^10.

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.

asalimpo:
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.

Sorry, I wanted to type the not equal sign.
I wanted to illustrate the bottleneck using those examples.

asalimpo:
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.

It's alright sir!