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SAT Math: Complex Exponent Rules
38+ practice questions in Praczo
What you need to know
The concept, explained
- 1
Mastering exponent combinations is critical. Rule 1: x^a * x^b = x^(a+b).
- 2
Rule 2: (x^a)^b = x^(a * b).
- 3
Rule 3: x^a / x^b = x^(a-b).
- 4
Rule 4: A negative exponent means reciprocal: x^(-a) = 1 / x^a.
- 5
Sometimes bases don't match initially (e.g., 9^x and 3^y). You must rewrite the larger base as a power of the smaller base: (3²)^x = 3^(2x) before applying rules.
Common mistakes
- ✗ Adding bases instead of just adding exponents (e.g., 2³ * 2² = 4⁵ — incorrect, it is 2⁵).
- ✗ Multiplying exponents when you should add them (e.g., x³ * x² = x^6 — incorrect, it is x⁵).
Try a sample question
SAT-style practice
If 3^x = 9^(y+1) and x = 6, what is the value of y?
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