Fractional Exponent: exponent expressed as a fraction (ex. 4^3/2 = (√4)³ = 2³ = 8)
Negative Exponent: exponent that is negative (ex. 4^-2 = 1 ÷ 4²; x^-3 = 1 ÷ x³)

RULES FOR MANIPULATING FRACTIONAL AND NEGATIVE EXPONENTS

1) x^1/2 = 4^1/3 --> x^(1/2)(6/1) = 4^(1/3)(6/1) --> x³ = 4² --> x³ = 16

2) x^-2= 2^-4 --> x^(-2/1)(-1/2) = 2^(-4/1)(-1/2) --> x¹ = 2² --> x = 4

3) x^-1/2 = 4^1/4 --> x^(-1/2)(-4/1) = 4^(1/4)(-4/1) --> x² = 4^-1 --> x² = 1/4 --> x = 1/2

TIP FOR FRACTIONAL AND NEGATIVE EXPONENT PROBLEMS
Focus on the form that the solution takes. On the SAT, you are often not asked to completely eliminate the exponents but to manipulate their form into something different than the original exponent.

SAMPLE PRACTICE QUESTION FOR FRACTIONAL AND NEGATIVE EXPONENTS

If (x + y)^-1 = (x + y)^-1/2 , then which of the following values could be the value of (x + y)?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

     Solution 1: Manipulating Exponents
     1) (x + y)^-1 = (x + y)^-1/2
     2) (x + y)^(-1/1)(-2/1) = (x + y)^(-1/2)(-2/1)
     3) (x + y)² = (x + y)¹

     So (x + y) can only equal 1 [Choice (A)].

     Solution 2: Using Plug-In
     1) (x + y)^-1 = (x + y)^-1/2
     2) Choice (A): (x + y) = 1

     So, 1^-1= 1^-1/2--> (1 ÷ 1) = (1 / √1) --> 1 = 1

SAT Math: Fractional and Negative Exponents

Lesson Includes:

—Math Terms for Fractional and Negative Exponents

—Rules for Manipulating Fractional and Negative Exponents

—Tip for Fractional and Negative Exponents

—Sample Practice Questions

—Practice Questions

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NEGATIVE & FRACTIONAL EXPONENTS REVIEW QUIZ

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