Hi, there! I'm happy to help with this. What is (1/16)^(-1/4)
Well, this one combines a few good exponent rules.
First of all:
(any positive number)^(any power at all) = a positive number
so, right away, answer (A) is out.
One BIG idea --- a negative exponent means: take the reciprocal.
a^(-n) = 1/(a^n)
(1/a)^(-n) = a^n
Thus, (1/16)^(-1/4) = 16^(1/4)
Another BIG idea --- a fractional exponent means take a root.
a^(1/2) = the square root of a
a^(1/3) = the cube root of a
a^(1/4) = the fourth root of a
So, 16^(1/4) equals the fourth root of 16. What number, when raised to the fourth power, equals 16? That number is 2, because 2^4 = 2x2x2x2 = 16.
Here's a challenging practice PS on laws of exponentshttp://gmat.magoosh.com/questions/725
The question at that link should be followed by a complete video solution when you submit your answer.
Does all this make sense? Please let me know if you have any questions.
Magoosh Test Prep