Exponent
Calculate powers and exponential expressions
How to use Exponent
- 1Enter the bottom number and the index to be applied.
- 2Select the index as positive, negative or fraction.
- 3View the results, note that the negative index is divided by the bottom.
How the index works
a^n = a x a x ...(n); a^-n = 1/ a^n; a^(1/n) = n + rootThe index indicates the number of times the bottom is multiplied; the negative index translates into a fraction, which is equal to the opening.
The index compresses the repetitive multiplication into a compact swarm, which is why it appears in growth, decay and scientific algorithms.
An an for n a multiplication. Core law: Add a multiplication index to the base (am x an = am+n), multiplication of the multiplier index for aluminum ((am)n = amn), negative index is the last (a-n = 1/an) and fraction index is the opening (a^(1/2) = a). These laws make it possible to simplify the majority of algebra expressions.
The chicken soup "a 1% improvement per day" is actually a mathematical fact: 1.01365 ≈ 37.78, 37 times the original 37 a year later; in turn 0.99365 ≈ 0.026, only 2.6% a year later. ** The difference between the two is not two times, but more than 1,400 times **, which is the terrible thing about index growth. Understanding the growth of the index is critical for the management of finance (recontribution), the prevention of disease (transmission rate), and the development of technology (Moor law).
| Bottom | Index | Result | Apply |
|---|---|---|---|
| 2 | 10 | 1,024 | 1 KB = 1024 bytes |
| 2 | 16 | 65,536 | 16 bit Depth / port cap |
| 2 | 32 | About 4.29 billion | 32-bit address space |
| 10 | 3 | 1,000 | kg = 1000 g |
| 10 | 9 | 1 billion | Giga prefix |
| e | 1 | 2.71828 | Natural constant |
| 1.01 | 365 | 37.78 | One percent of the year's profit per day. |
| 0.99 | 365 | 0.026 | A daily retreat of 1% of annual interest |
Common calculator results quick check
Frequently asked questions
What does negative mean?
is 1 divided by the base number of the timebar, so that 2^3 equals 1/8.
How do you fit in?
Keep the bottom unchanged, with an index added: a^m x a^n = a^ (m+n).
What's the score index?
The denominator is the number of roots; for example, x^(1/2) is the square root of x.
Why equal 1 (a ≠ 0)?
It can be derived from the index law: am ÷an = am-n. When m = n, the left is am ÷ am = 1, the right is a0, so a0 = 1. It can also be seen from a diminishing perspective: 23 = 8,22 = 4,21 = 2, divided by 2, so 20 = 1,2−1 = 0.5. Note that 00 is undefined.
How do you use the scientific algorithm?
Write a number in a form of 10n (1 ≤a < 10). For example, 3,000 000 = 3 x 106, 00045 = 4.5 x 10-4. Index n is positive for large and negative for decimal. Calculator displays 3E6 or 3e6. When processing astronomical numbers or microscales, the scientific algorithm is much more reliable than a long string of 0.