What is Exponent: Definition and 220 Discussions

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases:









{\displaystyle b^{n}=\underbrace {b\times \dots \times b} _{n\,{\textrm {times}}}.}
The exponent is usually shown as a superscript to the right of the base. In that case, bn is called "b raised to the nth power", "b raised to the power of n", "the nth power of b", "b to the nth power", or most briefly as "b to the nth".
One has b1 = b, and, for any positive integers m and n, one has bn ⋅ bm = bn+m. To extend this property to non-positive integer exponents, b0 is defined to be 1, and b−n (with n a positive integer and b not zero) is defined as 1/bn. In particular, b−1 is equal to 1/b, the reciprocal of b.
The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices.
Exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public-key cryptography.

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  1. L

    Help calculating this limit please

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  2. K

    I Derivation for the indicial exponent in the Frobenius method

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  3. codebpr

    A Does the Maximum Lyapunov exponent depend on the eigenvalues?

    I am currently reading this paper where on page 8, the authors say that: This correlates with Figure 8 on page 12. Does it mean that there is a real correlation between eigenvalues and Lyapunov exponents?
  4. brotherbobby

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  5. adamaero

    I Algebra equation with variable as exponent

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  6. P

    A Simple argument for critical exponent

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  7. docnet

    B Can we have a complex number in the exponent?

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  8. karush

    MHB Can Exponent Values Be Determined with One Equation and Two Variables?

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  9. L

    Cost Estimation capacity exponent formula

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  10. P

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  11. anemone

    MHB Unsolved Challenge: Natural logarithm and Exponent

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  12. anemone

    MHB Factorials and Exponent Challenge

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  13. morrobay

    B Obtaining a Future Numbers Increase With Exponent From Past Increase

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  14. Saracen Rue

    I Tetration except each repeated exponent increases by 1

    I was just wondering what the proper notation would be to describe an infinite power tower which has each repeated exponent increasing by a value of 1, like such; $$a^{{{{{{(a+1)}^{(a+2)}}^{(a+3)}}^{.}}^{.}}^{.}}$$
  15. I

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  16. V

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  17. SamRoss

    I Missing exponent in "Theoretical Minimum"?

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  18. V

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  19. navneet9431

    B 1 to the power of infinity, why is it indeterminate?

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  20. rude man

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  21. Algr

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  22. karush

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  23. YoungPhysicist

    B Triangle of Powers: Revolutionary Math Notation

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  24. R

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  25. Greg Bernhardt

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  26. S

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  27. R

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  28. A

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  29. H

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  30. onemic

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  31. quantumdude

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  32. Mr Davis 97

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  33. Z

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  34. M

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  35. Cjosh

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  36. Cjosh

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  37. ATY

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  38. E

    I Why time in formula accelarion has exponent two

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  39. K

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    Homework Statement A distance R is measured to be 3.400±0.003m. What is the relative uncertainty in R? 9×10-4 What is the relative uncertainty in R^-2? Homework EquationsThe Attempt at a Solution Relative uncertainty of R is 0.003/3.4=8.8e-4 Relative uncertainty of R^-2= -2(8.8e-4)=-1.76e-3...
  40. T

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  41. B

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  42. chwala

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  43. coolul007

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  44. S

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  45. B

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  46. Z

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  47. PhysicsBoyMan

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  48. D

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  49. mhsd91

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