Laws of Exponents

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Familiarize with these basic laws. Then, use the flashcards below to practice them and increase your speed and stamina using them.

Use Rule #1 above for these flash cards.

• x^a · x^b =
  x^{a + b}
• 2² · 2 =
  2^{2 + 1} = 2³ = 8
• 2² · 2² =
  2^{2 + 2} = 2⁴ = 16
• 2² · 2³ =
  2^{2 + 3} = 2⁵ = 32
• 2² · 2⁴ =
  2^{2 + 4} = 2⁶ = 64
• 2³ · 2⁴ =
  2^{3 + 4} = 2⁷ = 128
• 2³ · 2⁵ =
  2^{3 + 5} = 2⁸ = 256
• 2³ · 2⁶ =
  2^{3 + 6} = 2⁹ = 512
• 2³ · 2⁷ =
  2^{3 + 7} = 2¹⁰ = 1024
• 3² · 3² =
  3^{2 + 2} = 3⁴ = 81
• 3² · 3³ =
  3^{2 + 3} = 3⁵ = 243
• 3³ · 3³ =
  3^{3 + 3} = 3⁶ = 729

Use Rule #2 above for these flash cards.

• x^a / x^b =
  x^{a - b}
• 2³ / 2 =
  2^{3 - 1} = 2² = 4
• 2⁶ / 2³ =
  2^{6 - 3} = 2³ = 8
• 2⁸ / 2³ =
  2^{8 - 3} = 2⁵ = 32
• 3⁶ / 3² =
  3^{6 - 2} = 3⁴ = 81
• 3⁸ / 3³ =
  3^{8 - 3} = 3⁵ = 243
• 3⁸ / 3² =
  3^{8 - 2} = 3⁶ = 729
• 3⁹ / 3² =
  3^{9 - 2} = 3⁷ = 2,187

Use Rule #3 above for these flash cards.

• (x^a)^b =
  x^ab
• (2²)² =
  2^{2 × 2} = 2⁴ = 16
• (2²)³ =
  2^{2 × 3} = 2⁶ = 64
• (2⁴)² =
  2^{4 × 2} = 2⁸ = 256
• (2³)³ =
  2^{3 × 3} = 2⁹ = 512
• (2²)⁵ =
  2^{2 × 5} = 2¹⁰ = 1024
• (3²)² =
  3⁴ = 81
• (3²)³ =
  3⁶ = 729
• (5²)² =
  ⁴ = 625
• (5²)³ =
  5⁶ = 15,625