hitman,

There are no general rules for addition or subtraction of exponents(unlike multiplication and addition), instead on the GMAT almost all such problems are simplified using the distributive property of multiplication over addition:

\(a(b+c) = ab + ac\)

For example:

\(42 + 56 = (7)(6) + (7)(8) = 7(6+8) = 7(14) = 98\)

We use the same idea for exponent terms:

\(3^{11} - 3^{10} = (3^{10})(3) - 3^{10}(1) = 3^{10}(3 - 1) = 3^{10}(2)\)

Another example that I use with students:

\(2^{20} - 3(2^{18}) = 2^{18}(2^2 - 3) = 2^{18}(4 - 3) = 2^{18}\)

Here is a list of official GMAT problems that use the same general principle to solve these types of problems:

If you haven't taken the GMATPrep practice test, then skip the ones listed as Official GMATPrep.

1) Old GMAT Paper Test(Easy):

5-12-5-13-a-5-25-b-10-25-c-6-5-12-d-10-12-5-e-49552.html2) Official GMATPrep(Medium):

which-of-the-following-is-equal-to-the-value-of-60927.html3) Official GMAT Test(Medium):

what-is-the-greatest-prime-factor-of-2-100-2-96-a-2-b-70126.html4) Official GMAT Test(Hard):

if-5-x-5-x-3-124-5-y-what-is-y-in-terms-of-x-109080.html5) Official Guide GMAT 13th Edition(Hard):

the-value-of-2-14-2-15-2-16-2-17-5-is-130682.html6) Official GMATPrep Software(Hard):

what-is-the-greatest-prime-factor-of-104757.html7) Official GMATPrep(Hard):

if-3-x-3-x-1-162-then-x-x-1-a-12-b-16-c-20-d-44795.html8) Official GMAT Test(Medium):

if-2-x-2-x-2-x-2-x-2-n-what-is-x-terms-of-n-a-54074.html?fl=similar9) Official GMATPrep(Hard):

http://www.beatthegmat.com/gprep-2-2-2- ... 36087.html ; this can also be solved by using the concept of Geometric series.

10) Official GMATPrep(Hard):

if-2-x-2-x-2-3-2-13-what-is-the-value-of-x-130109.htmlI believe that is pretty much all of the Official GMAT questions on this subtopic, other than the ones on the real exam over the last few years.

Dabral