GMAT Prep Question--Exponents

[mindruna]

This has to be simple but I'm not understanding the process. Any tips would be great!


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


The official answer is 2^6 + 3^6

[gabriel]

This has to be simple but I'm not understanding the process. Any tips would be great!


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


The official answer is 2^6 + 3^6

.. the theory first ... x^a*x^b = x^(a+b) ..

.. now take a look at the expression .. 2^5 + 2^5 + 3^5 + 3^5 + 3^5 .. it can be changed to .. 2^5(1+1)+3^5(1+1+1) .. that is taking 2^5 and 3^5 common ..

.. so we have 2^5*(2) + 3^5*(3) = which according to the rule of exponents that i mentioned at the start is equal to 2^6 + 3^6 ..

[tanyajoseph]

2^5(2)+3^5(3)

Which is equivalent to 2^6+3^6
Reason: We already have 2^5 and now have an additional 2 which can be expressed as 2^6. Same applies to 3^5(3) where to the existing 3 set, there is an additional entry which implies 3 ^6(as there are 6 three's)
Hope that answers ur query.

[tanyajoseph]

And to answer the first part of how u get 2^5(2)+3^5(3)

Consider the given expression 2^5+2^5+3^5+3^5+3^5
Take out the common parts - 2^5(1+1) +3^5(1+1+1)
which can be written as 2^5(2)+3^5(3)