GRE Math formula sheet : Powers and Roots

Powers and Roots

Exponents

Notation:

Exponent Laws:

1 and 0 as bases:

                         1 raised to any power is 1. 0 raised to any nonzero power is 0

                         Any nonzero number to the power of 0 is 1:

Fractions as exponents:

Negative exponents:

Negative bases:

A negative number raised to an even power is positive; a negative number raised to an odd power is negative.

Odd/even exponents:

To raise 10 to any power, just put that many 0s after the 1:

a 1 with 5 zeros

Roots

Square roots of negative numbers (e.g.). They have no real solutions (they have imaginary solutions involving i, the square root of -1, but that definitely won’t be on the GRE.)

Perfect squares: 

Numbers with integers as their square roots: 4, 9, 16, etc.

To estimate square roots of numbers that aren’t perfect squares, just examine the nearby perfect squares. For example, to find  between 7 and 8.

Cube roots:

Simplifying roots:

Separate the number into its prime factors, and take out matching pairs:

Adding roots: