2 To The 8th Power
Exponents
The exponent of a number says how many times to use the number in a multiplication.
In 8two the "2" says to use 8 twice in a multiplication,
so eight2 = 8 × 8 = 64
In words: 82 could be chosen "eight to the power ii" or "8 to the 2nd power", or simply "8 squared"
Exponents are also called Powers or Indices.
Some more than examples:
Example: 53 = five × 5 × v = 125
- In words: 5three could be called "5 to the third power", "five to the power iii" or simply "5 cubed"
Example: 2iv = 2 × 2 × 2 × 2 = xvi
- In words: iiiv could be called "2 to the fourth power" or "2 to the power 4" or merely "two to the quaternary"
Exponents brand it easier to write and employ many multiplications
Example: 9half dozen is easier to write and read than ix × 9 × 9 × 9 × nine × 9
Yous can multiply whatsoever number past itself as many times as you desire using exponents.
Endeavor hither:
algebra/images/exponent-calc.js
And so in full general:
| an tells you to multiply a by itself, so at that place are north of those a'southward: |  |
Another Way of Writing Information technology
Sometimes people use the ^ symbol (above the half-dozen on your keyboard), as it is easy to type.
Example: 2^4 is the same every bit 2four
- ii^4 = 2 × 2 × 2 × 2 = xvi
Negative Exponents
Negative? What could be the opposite of multiplying? Dividing!
And then nosotros divide by the number each time, which is the same as multiplying by one number
Example: viii-1 = 1 8 = 0.125
We can go along on like this:
Example: 5-3 = 1 v × i 5 × 1 five = 0.008
But it is often easier to do it this style:
5-3 could also be calculated like:
1 v × 5 × five = 1 v3 = 1 125 = 0.008
Negative? Flip the Positive!
 | That last instance showed an easier manner to handle negative exponents:
|
More Examples:
| Negative Exponent | Reciprocal of Positive Exponent | Answer | ||
|---|---|---|---|---|
| 4-ii | = | 1 / 42 | = | ane/16 = 0.0625 |
| 10-3 | = | 1 / 103 | = | 1/1,000 = 0.001 |
| (-2)-three | = | 1 / (-2)three | = | 1/(-8) = -0.125 |
What if the Exponent is 1, or 0?
| ane | If the exponent is 1, and then you lot only accept the number itself (example 9i = 9) | |
| 0 | If the exponent is 0, then y'all go 1 (example ix0 = one) | |
| But what nigh 00 ? It could be either 1 or 0, and so people say it is "indeterminate". |
Information technology All Makes Sense
If you look at that table, you will see that positive, zero or negative exponents are really part of the same (fairly simple) pattern:
| Case: Powers of v | |||
|---|---|---|---|
| .. etc.. |  | ||
| 52 | five × v | 25 | |
| 51 | 5 | 5 | |
| 50 | i | 1 | |
| 5-1 | 1 5 | 0.2 | |
| 5-2 | i 5 × ane five | 0.04 | |
| .. etc.. | |||
Be Careful About Grouping
To avoid confusion, use parentheses () in cases like this:
| With () : | (−2)2 = (−ii) × (−2) = 4 |
| Without () : | −iiii = −(22) = −(2 × ii) = −4 |
| With () : | (ab)2 = ab × ab |
| Without () : | ab2 = a × (b)two = a × b × b |
305, 1679, 306, 1680, 1077, 1681, 1078, 1079, 3863, 3864
2 To The 8th Power,
Source: https://www.mathsisfun.com/exponent.html
Posted by: cruzsapeate.blogspot.com
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