🧮

Exponents, Logarithms, Complex Numbers & Matrices

132 cards · 🇺🇸 English

Exponent and logarithm rules, imaginary/complex numbers, and matrix basics.

algebraexponentslogarithmscomplex-numbersmatrices

Study all 132 cards for free

Flashcards, quizzes, pixel-art games and a daily review that remembers for you.

Study this deck free

Try the first 10 cards

1 / 10
Question

Exponentiation

Knew itLearning

Tap the card for the answer · swipe right if you knew it, left if not

Already have an account? Sign in

Cards

  1. 1Exponentiation
    An operation involving a base b and an exponent n, written as bⁿ
  2. 2What does bⁿ mean when n is a positive integer?
    The product of multiplying n bases: b × b × b × ... (n times)
  3. 3B²
    b squared (the square of b), because the area of a square with side b is b²
  4. 4B³
    b cubed (the cube of b), because the volume of a cube with side b is b³
  5. 53⁵
    243 (3 × 3 × 3 × 3 × 3)
  6. 6What does the word 'exponent' originate from?
    From Latin 'exponentem,' meaning 'to put forth'
  7. 7B⁰ equal to
    1 (for any nonzero b)
  8. 8B¹
    b (any number raised to the power 1 is itself)
  9. 9Multiplication rule for exponents
    bᵐ × bⁿ = b⁽ᵐ⁺ⁿ⁾ (when multiplying same base, add exponents)
  10. 10Division rule for exponents
    bᵐ / bⁿ = b⁽ᵐ⁻ⁿ⁾ (when dividing same base, subtract exponents)
  11. 11Power of a power rule
    (bᵐ)ⁿ = b⁽ᵐⁿ⁾ (multiply the exponents)
  12. 12(ab)ⁿ equal to
    aⁿ × bⁿ (distribute the exponent to both factors)
  13. 13(a/b)ⁿ equal to
    aⁿ / bⁿ (distribute the exponent to numerator and denominator)
  14. 14B⁻ⁿ equal to
    1 / bⁿ (negative exponent means reciprocal)
  15. 152⁻³
    1/8 (which is 1/(2³) = 1/8)
  16. 16B^(1/n)
    The nth root of b, written as ⁿ√b
  17. 17B^(1/2)
    √b (the square root of b)
  18. 18B^(1/3)
    ³√b (the cube root of b)
  19. 19B^(m/n)
    ⁿ√(bᵐ) or (ⁿ√b)ᵐ (nth root of b to the mth power)
  20. 20Is exponentiation commutative?
    No. For example, 2³ = 8 but 3² = 9
  21. 21Is exponentiation associative?
    No. For example, (2³)² = 64 but 2⁽³²⁾ = 512
  22. 22How is 2³² evaluated (order of operations)?
    Right-associative (top-down): 2⁽³²⁾ = 2⁹ = 512, not (2³)² = 64
  23. 230ⁿ for positive n
    0 (zero to any positive power is zero)
  24. 241ⁿ for any n
    1 (one to any power is one)
  25. 25(-1)²
    1 (negative times negative is positive)
  26. 26(-1)³
    -1 (odd power of -1 is negative)
  27. 27(-1)⁴
    1 (even power of -1 is positive)
  28. 28What pattern do powers of -1 follow?
    They alternate: (-1)ⁿ = 1 if n is even, -1 if n is odd
  29. 2910³
    1000 (1 followed by 3 zeros)
  30. 3010⁻⁴
    0.0001 (decimal point followed by 4 digits, last is 1)

And 102 more cards. Study the whole deck free

Articles about this deck

More Mathematics decks

See all
Study all 132 cards free