📝 Exponents Radicals

Part 1 of 7 — Exponent Rules

Product rule: aᵐ · aⁿ = aᵐ⁺ⁿ.

Quotient rule: aᵐ / aⁿ = aᵐ⁻ⁿ.

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Key Insight: Power rule: (aᵐ)ⁿ = aᵐⁿ.

SAT Tip: Power of a product: (ab)ⁿ = aⁿbⁿ.

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Negative & Zero Exponents

Part 2 of 7 — Negative & Zero Exponents

a⁰ = 1 for any a ≠ 0.

a⁻ⁿ = 1/aⁿ — move to denominator and make positive.

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Key Insight: (a/b)⁻ⁿ = (b/a)ⁿ — flip the fraction.

SAT Tip: Simplify step by step: apply rules, then convert negative exponents.

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Radical Expressions

Part 3 of 7 — Radical Expressions

√a = a^(1/2); ∛a = a^(1/3); ⁿ√a = a^(1/n).

Simplify radicals by factoring out perfect squares/cubes.

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Key Insight: Rationalize denominators: multiply by √a/√a.

SAT Tip: Add/subtract radicals: only combine like radicals (same radicand).

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Rational Exponents

Part 4 of 7 — Rational Exponents

a^(m/n) = ⁿ√(aᵐ) = (ⁿ√a)ᵐ.

Convert between radical and exponent form.

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Key Insight: Apply exponent rules to rational exponents.

SAT Tip: Example: 8^(2/3) = (∛8)² = 2² = 4.

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Scientific Notation

Part 5 of 7 — Scientific Notation

Scientific notation: a × 10ⁿ where 1 ≤ a < 10.

Large numbers: move decimal left, positive exponent.

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Key Insight: Small numbers: move decimal right, negative exponent.

SAT Tip: Multiply/divide: handle coefficients and powers of 10 separately.

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Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

Scientific notation: a × 10ⁿ where 1 ≤ a < 10.

Large numbers: move decimal left, positive exponent.

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Key Insight: Small numbers: move decimal right, negative exponent.

SAT Tip: Multiply/divide: handle coefficients and powers of 10 separately.

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Review & Applications

Part 7 of 7 — Review & Applications

Scientific notation: a × 10ⁿ where 1 ≤ a < 10.

Large numbers: move decimal left, positive exponent.

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Key Insight: Small numbers: move decimal right, negative exponent.

SAT Tip: Multiply/divide: handle coefficients and powers of 10 separately.

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