5 To The 2nd Power
Exponents
The exponent of a number says how many times to apply the number in a multiplication.
In 82 the "ii" says to apply viii twice in a multiplication,
so viii2 = 8 × 8 = 64
In words: 8ii could exist called "viii to the power two" or "8 to the second power", or simply "viii squared"
Exponents are also called Powers or Indices.
Some more than examples:
Case: 53 = v × five × v = 125
- In words: 5iii could exist called "v to the third ability", "five to the power three" or only "5 cubed"
Instance: twoiv = 2 × two × 2 × ii = 16
- In words: 24 could be chosen "2 to the fourth ability" or "2 to the power 4" or but "2 to the fourth"
Exponents make it easier to write and apply many multiplications
Example: 9vi is easier to write and read than 9 × 9 × nine × 9 × 9 × 9
You lot tin multiply any number by itself as many times as you lot desire using exponents.
Try here:
algebra/images/exponent-calc.js
So in general:
| anorthward tells y'all to multiply a by itself, and then there are n of those a's: |  |
Another Way of Writing It
Sometimes people use the ^ symbol (above the half dozen on your keyboard), as it is easy to type.
Example: ii^4 is the same as 24
- two^4 = 2 × 2 × ii × 2 = 16
Negative Exponents
Negative? What could be the opposite of multiplying? Dividing!
So we split by the number each time, which is the same every bit multiplying by ane number
Example: viii-1 = 1 8 = 0.125
Nosotros tin continue on like this:
Example: 5-3 = one 5 × one v × ane 5 = 0.008
Merely information technology is frequently easier to practise it this way:
5-3 could besides be calculated like:
1 v × five × 5 = 1 53 = 1 125 = 0.008
Negative? Flip the Positive!
 | That concluding instance showed an easier way to handle negative exponents:
|
More Examples:
| Negative Exponent | Reciprocal of Positive Exponent | Reply | ||
|---|---|---|---|---|
| 4-2 | = | 1 / fourii | = | ane/16 = 0.0625 |
| 10-iii | = | 1 / 10three | = | one/one,000 = 0.001 |
| (-2)-iii | = | i / (-ii)iii | = | one/(-eight) = -0.125 |
What if the Exponent is 1, or 0?
| 1 | If the exponent is ane, and so you lot just have the number itself (example 91 = 9) | |
| 0 | If the exponent is 0, then you lot get 1 (example 90 = one) | |
| But what virtually 00 ? Information technology could be either 1 or 0, and then people say it is "indeterminate". |
Information technology All Makes Sense
If you look at that table, y'all will see that positive, goose egg or negative exponents are actually function of the same (fairly unproblematic) pattern:
| Case: Powers of 5 | |||
|---|---|---|---|
| .. etc.. |  | ||
| fivetwo | 5 × 5 | 25 | |
| 5one | v | v | |
| 50 | 1 | ane | |
| v-i | 1 v | 0.2 | |
| five-ii | 1 5 × one v | 0.04 | |
| .. etc.. | |||
Be Careful About Grouping
To avoid confusion, utilize parentheses () in cases like this:
| With () : | (−2)two = (−ii) × (−ii) = 4 |
| Without () : | −ii2 = −(22) = −(2 × ii) = −iv |
| With () : | (ab)2 = ab × ab |
| Without () : | abtwo = a × (b)ii = a × b × b |
305, 1679, 306, 1680, 1077, 1681, 1078, 1079, 3863, 3864
5 To The 2nd Power,
Source: https://www.mathsisfun.com/exponent.html
Posted by: rosenbergequed1960.blogspot.com
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