✏️ Algebra — Expressions
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Laws of Exponents

Master the rules that govern exponential expressions.

The laws of exponents provide systematic rules for simplifying expressions involving powers. These rules apply to all real-number bases (with appropriate restrictions) and extend naturally to rational and negative exponents.

The Exponent Laws

Product Rule: xᵃ · xᵇ = xᵃ⁺ᵇQuotient Rule: xᵃ / xᵇ = xᵃ⁻ᵇPower Rule: (xᵃ)ᵇ = xᵃᵇZero Exponent: x⁰ = 1 (x ≠ 0)Negative Exponent: x⁻ᵃ = 1/xᵃ
xa⋅xb=xa+bxaxb=xa−b(xa)b=xabx^a \cdot x^b = x^{a+b} \qquad \frac{x^a}{x^b} = x^{a-b} \qquad (x^a)^b = x^{ab}
🧮Simplifying with Multiple Rules
Simplify (2x³y²)⁴ / (4x²y). Apply power rule: 2⁴x¹²y⁸ / (4x²y) = 16x¹²y⁸ / (4x²y) = 4x¹⁰y⁷.
(2x3y2)44x2y=16x12y84x2y=4x10y7\frac{(2x^3 y^2)^4}{4x^2 y} = \frac{16x^{12}y^8}{4x^2 y} = 4x^{10}y^7
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Remember This!

When simplifying complex expressions, apply the power rule first to eliminate parentheses, then use product/quotient rules. Keep track of each base separately.

✏️ Try It!

Simplify: (x⁵ · x³) / x⁴

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⚡Exponent Rules🔬Scientific Notation
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