Exponents & Radicals
Digital SAT Math (Advanced Math) — exponent rules, negative and fractional exponents, and simplifying radicals. Worked example and a common trap.
Exponents and radicals appear across the Digital SAT "Advanced Math" questions. The whole topic comes down to a small set of rules applied carefully.
Exponent rules
- Product:
xᵃ · xᵇ = xᵃ⁺ᵇ - Quotient:
xᵃ / xᵇ = xᵃ⁻ᵇ - Power of a power:
(xᵃ)ᵇ = xᵃᵇ - Negative:
x⁻ᵃ = 1 / xᵃ - Zero:
x⁰ = 1(for x ≠ 0)
Fractional exponents = radicals
x^(1/n) = ⁿ√x and x^(m/n) = ⁿ√(xᵐ).
Example: 8^(2/3) = (³√8)² = 2² = 4.
Worked example
Simplify (2x³)² · x⁻⁴.
(2x³)² = 4x⁶, then 4x⁶ · x⁻⁴ = 4x².
Common trap
(x + y)² is not x² + y². Expand it: x² + 2xy + y². The SAT deliberately offers x² + y² as a wrong answer. Also remember a negative exponent means reciprocal, not a negative number: 2⁻³ = 1/8, not −8.
SAT strategy
If you are unsure, plug in a simple number (like x = 2) into both the question and the answer choices and see which matches — a reliable check on Advanced Math questions.
Interactive Simulation
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Short Lesson Video
Mock Exam
Practice Quiz
Test yourself: instant results and explanations.
1. Simplify (2x³)² · x⁻⁴
2. What is 8^(2/3) ?
3. (x + y)² is equal to:
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