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Questions about trickier exponent questions?

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Questions about trickier exponent questions? [#permalink] New post 27 Jan 2008, 09:24
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Hi group, I have some questions about tricky exponenty questions:

1. What could X^(7x+3)^(x+3) be reduced to?
2. What does 1/4^(-1/4/5) reduce to?
3. What does 1/4^(-1/4/5)^(-1/4) reduce to?
4. what does 1/4*1/4^(-1/4/5)^(-1/4) reduce to?

Thanks group!
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Re: Questions about trickier exponent questions? [#permalink] New post 30 Jan 2008, 16:11
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bump for the masters
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Re: Questions about trickier exponent questions? [#permalink] New post 30 Jan 2008, 18:32
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dominion wrote:
Hi group, I have some questions about tricky exponenty questions:

1. What could X^(7x+3)^(x+3) be reduced to?
2. What does 1/4^(-1/4/5) reduce to?
3. What does 1/4^(-1/4/5)^(-1/4) reduce to?
4. what does 1/4*1/4^(-1/4/5)^(-1/4) reduce to?

Thanks group!



A) a^b^c = a^(b*c)
for eg. 2^2^3 = 2^6

B) a/b/c = (a/b)/c [IIRC - can someone confirm]
for eg. 1/2/3 = (1/2)/3 = (1/2)*(1/3) = 1/6

C) a^-b = (1/a) ^ b
for eg. 4 ^ -2 = (1/4) ^ 2

So:
1. X^(7x+3)^(x+3)
= X ^ (7x^2 + 24x + 9)

2. 1/4^(-1/4/5)
= 1/4 ^ (-1/20)
= 4 ^ (1/20), or the 20th root of 4

3. 1/4^(-1/4/5)^(-1/4)
= 1/4 ^ [(-1/20) * (-1/4)]
= 1/4 ^ (1/80), or the 80th root of 0.25

4. 1/4*1/4^(-1/4/5)^(-1/4)
Evaluate parenthesis first, then exponents then DMAS (division, multiplication etc) in priority. For similar priority (division for instance), go L->R (left to right):
= 1/4*(1/4 ^ (1/80))
= 1/4 ^ (1 + 1/80)
= 1/4 ^ (81/80)
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Re: Questions about trickier exponent questions? [#permalink] New post 30 Jan 2008, 19:27
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dominion wrote:
Hi group, I have some questions about tricky exponenty questions:

1. What could X^(7x+3)^(x+3) be reduced to?
2. What does 1/4^(-1/4/5) reduce to?
3. What does 1/4^(-1/4/5)^(-1/4) reduce to?
4. what does 1/4*1/4^(-1/4/5)^(-1/4) reduce to?

Thanks group!


I get the following

1: x^(7x+3)(x+3) ---> x^7x^2+24x+9

2: first simplify the ^-1/4/5 --> -1/20 --> 1/4^-1/20 --> 4^1/20 --> 20th root(4)

3: again simplify the ^'s first. --> -1/20--> so 4^1/20 then 1/20*-1/4 --> -1/80 --> so switch again 1/4^1/80

get 80th root (1/4)

4: same process as above I get 1/4*1/4^1/80. I think we can add the exponents here ( really don't know though). So 1+1/80 --> 81/80 --> 1/4^81/80 you can check this --> 1/4 comes out and your left with root 80 (1/4) So

I think 1/4^81/80 is ok.
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Re: Questions about trickier exponent questions? [#permalink] New post 30 Jan 2008, 23:04
nice group! ESC3NAM AND WALKER GET IN HERE :D
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Re: Questions about trickier exponent questions? [#permalink] New post 31 Jan 2008, 06:56
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dominion wrote:
Hi group, I have some questions about tricky exponenty questions:

1. What could X^(7x+3)^(x+3) be reduced to?
2. What does 1/4^(-1/4/5) reduce to?
3. What does 1/4^(-1/4/5)^(-1/4) reduce to?
4. what does 1/4*1/4^(-1/4/5)^(-1/4) reduce to?

Thanks group!


The above formulas need interpretation since they are ambiguous. Here is mine:

a^b^c = a^(b^c) -> 2^2^3 = 2^(2^3)=2^8 = 256
1/4/5 = 1/(4/5)=5/4 -> I'd never write 1/4/5 myself just because it's too ambiguous

here is a helpful formula: (1/a)^(-b) = a^b
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Re: Questions about trickier exponent questions? [#permalink] New post 31 Jan 2008, 13:22
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I really confuse such handwriting: 1/4*1/4^(-1/4/5)^(-1/4) :???

(1/4)^a or 1/(4^a)
(1/4)/5 or 1/(4/5)
(a^b)^c or a^(b^c)

too much freedom... :)
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Re: Questions about trickier exponent questions?   [#permalink] 31 Jan 2008, 13:22
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