➕ Algebra 1 · Exponents and Polynomials

Laws of Exponents: true or false

Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.

All statements and answers

• x³ · x⁴ = x¹²

  ✗ False. Add the exponents: x³⁺⁴ = x⁷.

• x⁸ ÷ x² = x⁶

  ✓ True. Subtract the exponents: 8 − 2 = 6.

• (x²)⁵ = x¹⁰

  ✓ True. Power of a power: multiply the exponents, 2 · 5 = 10.

• (3x)² = 3x²

  ✗ False. Both factors get squared: (3x)² = 9x².

• x³ + x³ = x⁶

  ✗ False. Adding like terms gives 2x³. The exponent stays the same.

• 2³ · 2² = 2⁵

  ✓ True. 8 · 4 = 32 = 2⁵, and the rule gives 3 + 2 = 5.

• To multiply powers with the same base, you add the exponents.

  ✓ True. That is the product rule.

• (x²)³ = x⁵

  ✗ False. Multiply, don’t add: (x²)³ = x⁶.

• Sneak peek: x⁵ ÷ x⁵ = x⁰ = 1 when x ≠ 0.

  ✓ True. Any nonzero number divided by itself is 1, and the quotient rule would give exponent 5 − 5 = 0. The next lesson shows that we define x⁰ = 1 so that the rule keeps working.

• 5x² · 2x³ = 10x⁵

  ✓ True. Multiply coefficients (5 · 2 = 10) and add exponents (2 + 3 = 5).