GMAT Number Properties Section 6: Exponents

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1a. Exponent Rules

Fundamentals:
Common Roots
These roots commonly appear on the GMAT and should be memorized to save time.

The 15 Must Know Exponent Rules

1.	z2 = z × z	To the 2 power is called "squared."
2.	z3 = z × z × z	To the 3 power is called "cubed."
3.	z0 = 1 -670 =1	Any number to the 0 power equals one
4.	z1 = z -671 = -67	Anything to the 1 power equals itself .
5.	(1/2)2 = 1/4 (1/2)3 = 1/8 (1/2)4 = 1/16	The higher exponent you take a positive fraction, the smaller the number becomes. (1/2)2 = 1/4 > (1/2)3 = 1/8 > (1/2)4 = 1/16
6.	x-n = 1/(xn) 3-2 = (1/3)2 = 1/9	A number taken to a negative exponent is a fraction gets put in the denominator with 1 on the top.
7.	(-2)2 = 4 (-2)4 = 16	A negative number taken to any even exponent value is always a positive value. Why? The negatives cancel themselves out. (-2)2 = -2 × -2 = +4 (-2)4 = 16 = -2 × -2 × -2 × -2 = +16
8.	(-)(22) = -4	Note: If you aren't squaring the negative sign, it stays negative (this rarely happens on the GMAT because you are usually taking a square of a variable). x2 = 4, where x = -2. This is technically (-2)2 = 4.
9.	(-2)-3 = 8	But, a negative number taken to any odd exponent value is always a negative value. Why? (-2)-3 = -2 × -2 × -2 = - 8
8.	21/2 =	A fractional exponent becomes a root equal to the value of the fraction.
10.	34 × 32 = 36 3(4 + 2) = 36	Add the exponents when multiplying two powers of the same base.
11.	36 ÷ 32 = 34 3(6 - 2) = 34	Subtract the exponents when dividing a power of a specified base by another power of the same base:
12.	(32)3= 36 3(2 × 3) = 36	Multiply the exponents when you raise a power to a power
13.	(xyz)2 = x2y2z2	The power of a product of factors is written by raising each factor to the specified power.
14.	(x/y)3 = x3/y3	The power of a fraction is written by raising the numerator and the denominator to the specified power.
15.	33 + 24 = 27 + 16 = 43	Exponents of different bases must be multiplied out and then combined.

Determine how many times a bacteria cell can divide in a 24 hour period. If you begin with one bacteria cell ready to divide, how many cells will be produced in 24 hours? (this type of bacteria divides once every six hours).

Fractional Exponents

Fractional exponents are equal to the root value.
2^1/2 = √2

4^1/2 = 2 because √4 = 2

Contents of Number Properties Chapter: Table of Contents   Section 1: Number Rules   Section 2: Consecutive Numbers   Section 3: Divisibility   Section 4: Fractions   Section 5: Decimals   Section 6: Exponents   Section 7: Roots & Radicals   Section 8: Sample Questions   Roots & Radicals

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