If you're not good with exponents, remember this rule: when in doubt, write it out.
If m=3, then the equation becomes:
(-2)^(2*3) = 2^(9-3)
which simplifies to:
(-2)^6 = 2^6.
Now write out each side of the equation:
(-2)^6 = (-2)(-2)(-2)(-2)(-2)(-2) = 64
2^6 = 2*2*2*2*2*2 = 64
So the two sides of the equation are equal.
Here's the rule that the problem is testing: when a negative number is raised to an even power, the result is always positive:
(-2)^2 = 4
(-3)^4 = 81
(-942)^108 = something too huge to determine, but we do know that the result will be positive because the exponent is even.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
