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 Author: questioner [ Tue Aug 17, 2010 12:49 pm ] Post subject: GMAT Algebra If a is a positive integer then 3²ª + 36ª / 2²ª =A. (9/4)ª + 9ª B. 9ª + 18ªC. 18ªD. 0E. 2 × 9ª(E) 3²ª + 36ª / 2²ª = 9ª + 36ª / 4ª = 9ª + (36/4)ª = 9ª + 9ª = 2 × 9ª, choice (E).Plugging in different values for a until all choices except one are eliminated is also an option.---------Where did the 9ª + 36ª / 4ª = 9ª + (36/4)ª = 9ª + 9ª = 2 × 9ª come from?

 Author: Gennadiy [ Tue Aug 17, 2010 1:12 pm ] Post subject: Re: math (test 2, question 8): algebra, exponents Let us follow the reasoning step-by-step and I'll be explaining in brief the properties of the exponents we use along the way. An extended explanation of a property you may find at the end of this post.Originally we have:3²ª + 36ª / 2²ª =Let us use the property nʷª = (nʷ)ª = (nª)ʷ, where n, w, a are positive integers.= (3²)ª + 36ª / (2²)ª =Then we calculate the numbers within brackets:= (9)ª + 36ª / (4)ª =Let us use the property nª / wª = (n / w)ª, where n, w, a are positive integers.= 9ª + (36/4)ª =Then we calculate the number within brackets:= 9ª + (9)ª =Adding two equal values is the same as multiplying it by 2, so at the end we get:= 2 × 9ª, the right answer is choice (E).-------------EXTENDED EXPLANATIONS for the PROPERTIES WE USED:n, w, a are positive integers.1. nʷª = (nʷ)ª = (nª)ʷWhy is it so?The definition of an exponent tells us that:nʷª = n × ... × n {wa times}(nʷ)ª = (n × ... × n {w times})ª = (n × ... × n {w times}) × ... × (n × ... × n {w times}) {a brackets} = n × ... × n {wa times}(nª)ʷ = (n × ... × n {a times})ʷ = (n × ... × n {a times}) × ... × (n × ... × n {a times}) {w brackets} = n × ... × n {aw times}We can see that all the formulas result in the same number of multiplied n.2. nª / wª = (n / w)ªWhy is it so?The definition of an exponent tells us that:nª / wª = (n × ... × n {a times}) / (w × ... × w {a times}) = (n/w) × ... × (n/w) {a times} = (n / w)ª

 Author: questioner [ Wed Sep 15, 2010 4:05 am ] Post subject: Re: math (test 2, question 8): algebra, exponents Why isn't (36ª / 4ª) = 9? When we divide exponents I thought we subtract?

 Author: Gennadiy [ Wed Sep 15, 2010 4:14 am ] Post subject: Re: math (test 2, question 8): algebra, exponents We subtract exponents when we deal with the same base, e.g. 4²ª / 4 ª = 4ª. In this case the bases differ. Take a look at proper calculations once again:36ª / 4ª = (36/4)ª = 9ªor36ª / 4ª = (4 × 9)ª / 4ª = (4ª × 9ª) / 4ª = 9ª

 Author: questioner [ Tue Nov 02, 2010 3:42 am ] Post subject: Re: math (test 2, question 8): algebra, exponents How is answer C different from answer E?

 Author: Gennadiy [ Tue Nov 02, 2010 3:45 am ] Post subject: Re: math (test 2, question 8): algebra, exponents C. 18ªE. 2 × 9ª18ª = (2 × 9)ª = 2ª × 9ª > 2 × 9ª (if a > 1)

 Author: questioner [ Mon Feb 21, 2011 7:26 pm ] Post subject: Re: math (test 2, question 8): algebra, exponents Can you explain why 9ª + 9ª doesn't go to 2(9ª) = 18ª?

 Author: Gennadiy [ Mon Feb 21, 2011 7:31 pm ] Post subject: Re: math (test 2, question 8): algebra, exponents 2 × 9ª = 2 × (9 × 9 × ... × 9)18ª = (2 × 9)ª = 2ª × 9ª = (2 × 2 × ... × 2)(9 × 9 × ... × 9)

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