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
Reformatting a number
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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)
GMAT assassins aren't born, they're made,
Rich
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)
GMAT assassins aren't born, they're made,
Rich
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
(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