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Exponent Rules and Exponential Structure

SAT MathAdvanced MathFoundation

Rewrite powers without confusing products, powers, and sums.

What you need to know

  • For the same base, multiplication adds exponents and division subtracts them.
  • (aᵐ)ⁿ = aᵐⁿ.
  • A negative exponent means reciprocal; an exponent of zero gives 1 for a nonzero base.
  • Exponent rules do not distribute over addition.

The AYLOTI method

  1. Identify product, quotient, or power structure.
  2. Apply one exponent rule at a time.
  3. Rewrite with positive exponents if requested.
  4. Check with a simple numerical base.

AYLOTI • Sir Hunain Zia • SAT Score 1594/1600 • 154 Total A Grades (Personal), 11 World Records, 7 Distinctions

Worked example

Simplify (x³y⁻²)² ÷ x.

  1. Power: x⁶y⁻⁴.
  2. Divide by x: x⁵y⁻⁴.
  3. Positive exponent form: x⁵/y⁴.

Answer: x⁵/y⁴.

Common SAT traps

  • Turning (a + b)² into a² + b².
  • Adding exponents when raising a power to a power.
  • Dropping the reciprocal meaning of a negative exponent.
Quick check

Simplify a⁵/a².

a³, for a ≠ 0.

Before you move on

  • Explain the core rule without looking back.
  • Redo the worked example using your own steps.
  • Write the trap you are most likely to fall for.
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