2 To The 3rd Power
Exponents
The exponent of a number says how many times to use the number in a multiplication.
In viiiii the "ii" says to use 8 twice in a multiplication,
and then viiitwo = 8 × 8 = 64
In words: eight2 could be chosen "8 to the power ii" or "8 to the second power", or simply "8 squared"
Exponents are also called Powers or Indices.
Some more examples:
Example: 53 = 5 × 5 × 5 = 125
- In words: 5three could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"
Instance: 24 = 2 × 2 × 2 × 2 = 16
- In words: 24 could be called "ii to the fourth ability" or "2 to the power 4" or simply "ii to the 4th"
Exponents make information technology easier to write and utilize many multiplications
Example: 96 is easier to write and read than 9 × ix × nine × 9 × 9 × ix
You tin can multiply any number past itself every bit many times equally you want using exponents.
Try hither:
algebra/images/exponent-calc.js
So in general:
| adue north tells you to multiply a by itself, so there are n of those a's: |  |
Another Way of Writing It
Sometimes people apply the ^ symbol (above the 6 on your keyboard), every bit it is easy to type.
Example: two^4 is the same equally 24
- 2^4 = 2 × 2 × 2 × 2 = 16
Negative Exponents
Negative? What could be the opposite of multiplying? Dividing!
So we split up by the number each time, which is the same every bit multiplying by i number
Case: viii-1 = 1 8 = 0.125
We tin can keep on like this:
Case: 5-iii = one 5 × 1 5 × i 5 = 0.008
Only information technology is often easier to do it this way:
v-3 could also be calculated like:
1 5 × 5 × v = 1 53 = 1 125 = 0.008
Negative? Flip the Positive!
 | That last case showed an easier mode to handle negative exponents:
|
More Examples:
| Negative Exponent | Reciprocal of Positive Exponent | Answer | ||
|---|---|---|---|---|
| 4-two | = | 1 / 42 | = | one/sixteen = 0.0625 |
| 10-3 | = | 1 / 10three | = | one/1,000 = 0.001 |
| (-two)-3 | = | 1 / (-2)three | = | 1/(-eight) = -0.125 |
What if the Exponent is 1, or 0?
| i | If the exponent is 1, and so you lot just take the number itself (example ixane = 9) | |
| 0 | If the exponent is 0, then yous get one (instance 90 = 1) | |
| But what nearly 00 ? Information technology could be either one or 0, and and so people say it is "indeterminate". |
It All Makes Sense
If you wait at that table, you volition run across that positive, zero or negative exponents are actually part of the aforementioned (fairly elementary) pattern:
| Example: Powers of 5 | |||
|---|---|---|---|
| .. etc.. |  | ||
| 52 | 5 × five | 25 | |
| 51 | v | 5 | |
| v0 | i | ane | |
| 5-1 | 1 5 | 0.two | |
| v-2 | 1 5 × ane v | 0.04 | |
| .. etc.. | |||
Be Careful About Grouping
To avoid confusion, utilise parentheses () in cases similar this:
| With () : | (−2)2 = (−2) × (−two) = iv |
| Without () : | −two2 = −(two2) = −(two × 2) = −4 |
| With () : | (ab)ii = ab × ab |
| Without () : | ab2 = a × (b)ii = a × b × b |
305, 1679, 306, 1680, 1077, 1681, 1078, 1079, 3863, 3864
2 To The 3rd Power,
Source: https://www.mathsisfun.com/exponent.html
Posted by: mirandacoulp1949.blogspot.com
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