Math: Exponents Addition and Subtraction rules : GMAT Quantitative Section
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# Math: Exponents Addition and Subtraction rules

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26 Dec 2009, 12:02
Hello Guys,

What are the rules on adding and subtracting exponents?

For example: 2^5+2^5+2^5+3^5+3^5?

Is there a quick way to solve this?

(I know the multiplication, division and exponent rules on exponents.)

Cheers,
MathFear
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26 Dec 2009, 14:41
It would go this way:

$$2^5+2^5+2^5+3^5+3^5 = (2^5+2^5+2^5)+(3^5+3^5) =$$

$$3*2^5+2*3^5 = 2*3* (2^4+3^4) =$$

$$6 * (16+81) = 6 * 97 = 6*(100-3) = 600 - 18 = 582$$
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10 Jan 2010, 03:56
walker wrote:
It would go this way:

$$2^5+2^5+2^5+3^5+3^5 = (2^5+2^5+2^5)+(3^5+3^5) =$$

$$3*2^5+2*3^5 = 2*3* (2^4+3^4) =$$

$$6 * (16+81) = 6 * 97 = 6*(100-3) = 600 - 18 = 582$$

Hi walker, thank you for your response!

However, I noticed that I didn't copy the question right.

I meant:

2^5 + 2^5 + 3^5 + 3^5 + 3^5

And a Math guy showed me a fast way to calculate this. For me this is a typical trick I'd fall for. I'll just post the fast solution, for my fellow mathn00bs

2 * 2^5 = 2^6 (Because 2 = 2^1 and when multiplying exponents one needs to add them up.)
3 * 3^5 = 3^6 ( // )

So 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2^6 + 3^6 (This was the answer they were looking for in the question)
Re: Math: Exponents Addition and Subtraction rules   [#permalink] 10 Jan 2010, 03:56
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