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Reformatting a number

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Reformatting a number

by Nonnos123 » Sat Jun 02, 2018 10:59 pm
Guys, I have just started working on Gmat and came across an issue that I just can't get my head around.

The following:

6^5x5^6 ... would be when reformatting : (6x5)^5 x 5 or (30)^5 x 5

Could anyone please explain to me the general rule for rewriting this function into one of the second ones?

Thanks a lot in advance
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by [email protected] » Sun Jun 03, 2018 10:18 am
Hi Nonnos123,

When multiplying numbers together, it doesn't matter which number comes first. For example:

(2)(3)(4) = (3)(4)(2)

In that same way, you can 'rewrite' either of those calculations and still end up with the same result. For example:

(2)(3)(4) = (3)(4)(2)
(6)(4) = (3)(8)

The same idea applies to the example that you presented:
(6^5)(5^6) = (6)(6)(6)(6)(6)(5)(5)(5)(5)(5)(5)

We can multiply a number of those individual 6s and 5s and 'rewrite' the calculation....

(6)(6)(6)(6)(6)(5)(5)(5)(5)(5)(5)
(30)(30)(30)(30)(30)(5)
(30^5)(5)

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by Nonnos123 » Sat Jun 09, 2018 6:53 pm
Makes a lot of sense now! Thank u!
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answer

by jaetpu » Tue Jun 19, 2018 11:35 pm
Your expression can be modified by commutative and associative properties.


(6^5)*(5^6)
= 6^5 * 5^5 * 5
= (6*5)^5 * 5
You can combine 6^5 and 5^5 into (6*5)^5 because both terms have the same power. Notice that 5^6 is higher powered than 6^5. You can only combine the two terms up to the lesser power (5 in this case), which is why 5 is multiplied outside of the resulting exponent.



you can also review properties of multiplication here
https://www.khanacademy.org/math/pre-al ... rty-review
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