exponents rule

[Ruben]

Hi Everyone,

I am trying to understand what rules applies here. If t=3^n and n=3^(n-2)
how does t become t= 3^(3n-6) or 3^3(n-2).

It seems to me that n=3^(n-2) equals to 3^/ 3^2, right?

Thanks

[shaji]

Hi Everyone,

I am trying to understand what rules applies here. If t=3^n and n=3^(n-2)
how does t become t= 3^(3n-6) or 3^3(n-2).

It seems to me that n=3^(n-2) equals to 3^/ 3^2, right?

Thanks

BOTH STATEMENTS ARE INCORRECT!!!
If t=3^n and n=3^(n-2) ;
how does t become t= 3^(3n-6) or 3^3(n-2). ---INCORRECT
n=3^(n-2) equals to 3^/ 3^2, right?----INCORRECT

Solve for n; n=3^(n-2)....n=3
therfore t=3^3=27.

[StaceyKoprince]

If you were to substitute n into the t equation, you'd get:

t = 3^(3^(n-2))
(you might want to write that out on paper, as the formatting here in the forums makes that hard to read)

When you have a power raised to a power, the way you simplify is to multiply the two powers together. So you'd multiple 3 times n-2 to get:
t=3^(3n-6)

If you wanted to, you could then factor a 3 out of the exponential expression:
t=3^[3(n-2)]

You could also split the two terms being multiplied in the exponents in this way:
t=[3^3]*[3^(n-2)]
t = 9 * 3^(n-2)

As Shaji points out, the original n equation given only contains n as a variable, so you could indeed solve for n:
n = 3^(n-2)
n = (3^n)/3^2
9n = 3^n

I doubt the above would show up on the test because you'd either need to just "see" that n=3 or you'd need to use logs or a calculator (or both) to solve this thing.

By the way, if you take that 3 and plug it into the manipulation I ended up with above, look what you'd get:
t = 9 * 3^(n-2)
t = 9 * 3^(3-2)
t = 9*3^1
t = 9*3
t=27

Shaji - be careful - Ruben's first statement was correct, not incorrect. Please also just generally be careful about tone. In "Internet-speak," posting entire sentences in capital letters is equivalent to yelling - as though you are upset with someone or think they're in danger. :) I know you were just using it for emphasis here, but please be aware of the common usage of all caps on the Internet. One word = emphasis. Entire sentences = yelling.

Ruben, speaking of your second statement, is there a typo there? You wrote "3^/ 3^2" but it doesn't make sense to have a ^ (indicating an exponent) immediately followed by a division sign.

[Ruben]

Steacy,

Thanks a lot for the explanation. I have been trting to get straight these exponents rules for 2 weeks!

You were right, 3^3^(n-2) is the correct question, mine was a typo.

Best,

Ruben

[rfernandez]

We're glad it helped!

[erjamit]

I have a doubt here.

(a^b)^c = a^(bc)

but why is a^b^c = a^(bc)

e.g. (2^2)^4 = 2^(8)

but shouldn't 2^2^4 = 2^16 and not 2^(8)...

can anyone explain am I making any mistake here.

[RonPurewal]

I have a doubt here.

(a^b)^c = a^(bc)

but why is a^b^c = a^(bc)

e.g. (2^2)^4 = 2^(8)

but shouldn't 2^2^4 = 2^16 and not 2^(8)...

can anyone explain am I making any mistake here.

well, the biggest issue is that it's difficult to write exponents on this forum in the first place, let alone exponents that are embedded in other exponents. that is just awful.

but, as a mathematician, i'll inform you:
if something is written with embedded exponents, then the exponents within the exponents are performed first. this is really just an extension of the rule stating that operations within parentheses are performed before those outside parentheses (where the exponents are enclosed by imagined parentheses).
take a look at this page; in the first expression, e^e^e^79, the first exponential to be performed is e^79.

hth