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Need help with exponents

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Newbie | Next Rank: 10 Posts
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by mmcleod » Thu Apr 08, 2010 7:12 am
Does anyone know a good website that explains the different fundamentals of exponents. I have a basic understanding, but I definitely need to improve. Here are a couple of problems that I'm struggling with, so if anyone can provide a step-by-step solution, that would be great!

10^8 - 10^2
-----------------
10^7 - 10^4

The Answer = 10

also...

a^2 - b^2
--------------
b - a

The Answer = -a-b
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Source: — Quantitative Reasoning |
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by kstv » Thu Apr 08, 2010 9:15 am
10^8 - 10^2/10^7 - 10^4
10^8 - 10^2 = 10²(10^6-1) - Numerator N
10^7 - 10 ^4 = 10(10^6-10³) - Denominator D
assume 10³ = a so N = 10²(a²-1) and D = 10( a²-a)
10^6 = (10^3)^2
10²(a+1)(a-1)
---------------------
10 a (a-1)
10(a+1)/a but a = 10³
10(1001)/1000 = 1001/100 = 10.01

(a³)² = a ^6
a³xa² = a^5 = a(²+³)
a-¹= 1/a¹ etc
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