MathAdvanced MathHigh frequency
SAT Math: Fractional Exponents and Radicals
33+ practice questions in Praczo
What you need to know
The concept, explained
- 1
A fractional exponent x^(a/b) is equivalent to the b-th root of x^a: √(x^a) with root index b.
- 2
The top of the fraction is the Power; the bottom is the Root. (Think: roots of a tree are at the bottom).
- 3
x^(1/2) = √x. x^(1/3) = ∛x.
- 4
You can apply standard exponent rules (adding, subtracting, multiplying exponents) to fractional exponents just like integers.
- 5
When simplifying complex radical expressions, converting them to fractional exponents first often makes the math much clearer.
Common mistakes
- ✗ Flipping the numerator and denominator: thinking x^(2/3) is the square root of x cubed, rather than the cube root of x squared.
- ✗ Applying the exponent only to the variable and not the coefficient: (8x)^(1/3) is 2 * x^(1/3), whereas 8x^(1/3) is just 8 * x^(1/3).
Try a sample question
SAT-style practice
Which of the following is equivalent to x^(5/2)?
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