McGraw-Hill Education GRE 2019

The previous example illustrates the following general principle: An even exponent

will hide the sign of the base.

In other words, whether the base is positive or negative, when it is raised to an

even power, the result will be positive. This is because an even number of negative

factors will always cancel out to create a positive product.

The flip-side of this fact concerns odd exponents. An odd exponent will preserve

the sign of the base.

For example, if x^3 = −8, then there is just one solution for x: −2. Notice that 2 is

not a solution for x because if you plug it back into the equation, you arrive at

(2)^3 = 8, not −8.

Base of 0, 1, and −1

■ When a base of zero is raised to any power, the result is zero: 0^2 = 0

■ When 1 is raised to any power, the result is 1: 1^10 = 1; 1−30 0 = 1

■ When −1 is raised to an even power, the result is 1. When −1 is raised to an

odd power, the result will be −1: −1^10 = 1; −1−303 = −1

Fractional Base

■ When a positive proper fraction (a number between 0 and 1) is raised to a

power, an interesting property results: the resulting value is less than the

original base:

(^13 )^2 = (^13 )(^13 ) =^19

1

9 <

1

3

Compare the preceding to what happens when you raise an integer base to a

power:

52 = (5)(5) = 25

25 > 5

■ When a fraction is raised to a power, the exponent distributes to the

numerator and denominator of that fraction: (^32 )^4 =^3244 =^8116.

Exponent Rules

Most situations with exponents will require knowledge of basic exponent rules. A

good rule of thumb is that most exponent rules concern situations where either the

base or the exponent is the same and where you’re either multiplying or dividing.

Multiplying Exponents with the Same Base: Add the Exponents

■ When multiplying exponential terms with the same base, keep the base and

add the exponents: (3^5 )(3^3 ) = 3(5+3). To understand why you are adding the

exponents, write out 3^5 and 3^3. Notice that you arrive at: (3 × 3 × 3 × 3 × 3)

(3 × 3 × 3). This leaves you with 3 multiplied by itself 8 times. Thus 3^8.

270 PART 4 ■ MATH REVIEW

03-GRE-Test-2018_173-312.indd 270 12/05/17 11:54 am