Exponents

[fpere018]

How do you do to add big exponents with same base

2^35+2^16+2^26....

the answer is given with an exponent... the idea is the same base with very large numbers that it would take forever to solve it...How would you go about doing this?

Thanks

[LazyNK]

Hi fpere,
In my opinion, there is no "generic" answer to your question. You might really have to see based on the question, how to simplify the addition/subtraction of the exponents, and there could be many different scenarios, where a different technique could work.

Specifically, for the problem you mention, we can add as follows :
(Assuming only 3 terms in the adddition)-

2^35+2^16+2^26= 2^16*(2^19+1+2^10)=2^16*(1+2^10*(2^9+1))= 2^16*(1+1024*513) [ It might come handy to remember all powers of 2 uptill may be 2^12]
=525313*2^16

But this seems to be a problem where you still had to do the calculation of 1024*513, Normally you should get something more "regular".
-NK

[jnelson0612]

How do you do to add big exponents with same base

2^35+2^16+2^26....

the answer is given with an exponent... the idea is the same base with very large numbers that it would take forever to solve it...How would you go about doing this?

Thanks

Generally you express every expression in terms of the smallest term.

For example, here our smallest term is 2^16. Let's express each term in terms of 2^16.

Thus, we get:
2^19(2^16) + 1(2^16) + 2^10(2^16).

We can rewrite that as (2^19 + 1 + 2^10)(2^16).

Usually at this point we would be able to add the first part to obtain an integer. For example, if instead we had:
(2^3 + 1 + 2^4) (2^16)
we would then have:
(8 + 1 + 16) (2^16), or 25(2^16). This is how the GMAT usually handles such problems.