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exponents - no clue

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by gian-28 » Tue Jul 03, 2007 12:58 pm
does anyone know how to solve this problem? it's totally freaking me out...

(1/5)^m *(1/4)^18=1/2(10)^35

I don't even know how to approach this one. it's the first problem of a practice test.. :evil:
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by givemeanid » Tue Jul 03, 2007 3:39 pm
(1/5)^m * (1/4)^18 = 1/2 * 1/(10)^35

(1/5)^m = 1/2 * (1/10)^35 / (1/4)^18
= (4)^18 * 1/ 2 * (1/10)^35
= (4/10)^18 * 1/2 * (1/10)^17
= (2/5)^18 * 1/2 * (1/10)^17
= (1/5)^18 * 2^18 * 1/2 * (1/10)^17
= (1/5)^18 * 2^17 * (1/10)^17
= (1/5)^18 * (2/10)^17
= (1/5)^18 * (1/5)^17
= (1/5)^35

m = 35
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by sykedaddy » Wed Jul 04, 2007 1:37 pm
Easiest way for me was to rewrite...I just dislike fractions...

(1/5)^m *(1/4)^18=1/2(10)^35

(5)^-m * (2)^-36 = (2)^-1 * (2)^-35 * (5)^-35

..........................= (2)^-36 * (5)^-35

take out both (2)^-36 and

5^-m = 5^-35
No WAMMYs!!
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by II » Sat Dec 29, 2007 8:31 am
givemeanid wrote:(1/5)^m * (1/4)^18 = 1/2 * 1/(10)^35

(1/5)^m = 1/2 * (1/10)^35 / (1/4)^18
= (4)^18 * 1/ 2 * (1/10)^35
= (4/10)^18 * 1/2 * (1/10)^17
= (2/5)^18 * 1/2 * (1/10)^17
= (1/5)^18 * 2^18 * 1/2 * (1/10)^17
= (1/5)^18 * 2^17 * (1/10)^17
= (1/5)^18 * (2/10)^17
= (1/5)^18 * (1/5)^17
= (1/5)^35

m = 35
Apologies for the basic question, but how did you get from the question:

(1/5)^m *(1/4)^18=1/2(10)^35
to
(1/5)^m * (1/4)^18 = 1/2 * 1/(10)^35

The right hand side of the equation starts with 1/2(10)^35
And you have it down as 1/2 * 1/(10)^35
why ?

Thanks in advance.
II
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