how to find the exponent of a number
Exponents
The exponent of a number says how many times to use the number in a multiplication.
In 82 the "2" says to use viii twice in a multiplication,
so 82 = viii × 8 = 64
In words: 8ii could be called "eight to the power 2" or "8 to the second power", or but "eight squared"
Exponents are likewise chosen Powers or Indices.
Some more examples:
Example: five3 = 5 × v × 5 = 125
- In words: vthree could be called "v to the third ability", "5 to the power 3" or merely "5 cubed"
Example: iiiv = 2 × 2 × 2 × ii = 16
- In words: ii4 could be called "2 to the fourth power" or "ii to the power 4" or just "2 to the fourth"
Exponents go far easier to write and employ many multiplications
Example: 96 is easier to write and read than nine × 9 × ix × nine × nine × 9
Yous tin can multiply any number by itself equally many times as you desire using exponents.
Try hither:
algebra/images/exponent-calc.js
So in general:
| an tells yous to multiply a past itself, and so in that location are n of those a'south: |  |
Another Way of Writing It
Sometimes people use the ^ symbol (above the 6 on your keyboard), as information technology is easy to type.
Example: ii^iv is the same as 2four
- 2^4 = ii × 2 × 2 × 2 = sixteen
Negative Exponents
Negative? What could be the opposite of multiplying? Dividing!
And then we separate by the number each time, which is the same equally multiplying by 1 number
Case: 8-1 = 1 8 = 0.125
We can continue on like this:
Example: 5-3 = i v × 1 5 × 1 5 = 0.008
But it is often easier to practice it this way:
five-three could also exist calculated like:
1 five × v × 5 = one 5three = 1 125 = 0.008
Negative? Flip the Positive!
 | That last example showed an easier way to handle negative exponents:
|
More Examples:
| Negative Exponent | Reciprocal of Positive Exponent | Respond | ||
|---|---|---|---|---|
| 4-2 | = | one / fourtwo | = | ane/sixteen = 0.0625 |
| x-iii | = | 1 / 10three | = | 1/1,000 = 0.001 |
| (-2)-3 | = | 1 / (-ii)iii | = | 1/(-8) = -0.125 |
What if the Exponent is 1, or 0?
| 1 | If the exponent is 1, and then you lot simply have the number itself (case 91 = 9) | |
| 0 | If the exponent is 0, then you get 1 (case 90 = 1) | |
| But what about 00 ? It could be either 1 or 0, and then people say it is "indeterminate". |
It All Makes Sense
If you await at that tabular array, you will see that positive, zippo or negative exponents are really part of the same (fairly simple) pattern:
| Example: Powers of 5 | |||
|---|---|---|---|
| .. etc.. |  | ||
| fiveii | 5 × 5 | 25 | |
| v1 | 5 | 5 | |
| v0 | 1 | one | |
| 5-1 | i 5 | 0.ii | |
| 5-2 | i 5 × 1 5 | 0.04 | |
| .. etc.. | |||
Exist Careful Well-nigh Grouping
To avoid confusion, apply parentheses () in cases similar this:
| With () : | (−2)2 = (−two) × (−two) = 4 |
| Without () : | −ii2 = −(2ii) = −(two × 2) = −4 |
| With () : | (ab)two = ab × ab |
| Without () : | ab2 = a × (b)2 = a × b × b |
305, 1679, 306, 1680, 1077, 1681, 1078, 1079, 3863, 3864
Source: https://www.mathsisfun.com/exponent.html
Posted by: strattonthemy1953.blogspot.com
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