Note: Many pre-HTTP/1.1 user agents do not understand the 303 status. When interoperability with such clients is a concern, the 302 status code may be used instead, since most user agents react to a 302 response as described here for 303. 10.3.5 304 Not Modified. Definition – What is an exponent? An exponent is the number of times to multiply a number by itself. Write an exponent as a raised number. In the number 2 4 (2 to the exponent 4, or 2 to the power of 4), the ‘4’ is the exponent. Find the value of 5 to the third power. Let me rewrite that. We have 5 to the third power. Now, it's important to remember, this does not mean 5 times 3.
The exponent of a number says how many times to use the number in a multiplication.
In 82 the '2' says to use 8 twice in a multiplication,
so 82 = 8 × 8 = 64
In words: 82 could be called '8 to the power 2' 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: 53 could be called '5 to the third power', '5 to the power 3' or simply '5 cubed'
Example: 24 = 2 × 2 × 2 × 2 = 16
- In words: 24 could be called '2 to the fourth power' or '2 to the power 4' or simply '2 to the 4th'
Exponents make it easier to write and use many multiplications
Example: 96 is easier to write and read than 9 × 9 × 9 × 9 × 9 × 9
You can multiply any number by itself as many times as you want using exponents.
Try here:
In General
So in general:
| an tells you to multiply a by itself, so there are n of those a's: |
Another Way of Writing It
Sometimes people use the ^ symbol (above the 6 on your keyboard), as it is easy to type.
Example: 2^4 is the same as 24
- 2^4 = 2 × 2 × 2 × 2 = 16
Negative Exponents
Negative? What could be the opposite of multiplying? Dividing!
So we divide by the number each time, which is the same as multiplying by 1number
We can continue on like this:
Example: 5-3 = 15 × 15 × 15 = 0.008
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But it is often easier to do it this way:
5-3 could also be calculated like:
15 × 5 × 5 = 153 = 1125 = 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 | Answer | ||
|---|---|---|---|---|
| 4-2 | = | 1 / 42 | = | 1/16 = 0.0625 |
| 10-3 | = | 1 / 103 | = | 1/1,000 = 0.001 |
| (-2)-3 | = | 1 / (-2)3 | = | 1/(-8) = -0.125 |
What if the Exponent is 1, or 0?
| 1 | If the exponent is 1, then you just have the number itself (example 91 = 9) |
| 0 | If the exponent is 0, then you get 1 (example 90 = 1) |
| But what about 00 ? It could be either 1 or 0, and so people say it is 'indeterminate'. |
It 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:
| Example: Powers of 5 | |||
|---|---|---|---|
| .. etc.. | |||
| 52 | 5 × 5 | 25 | |
| 51 | 5 | 5 | |
| 50 | 1 | 1 | |
| 5-1 | 15 | 0.2 | |
| 5-2 | 15 × 15 | 0.04 | |
| .. etc.. | |||
Be Careful About Grouping
To avoid confusion, use parentheses () in cases like this:
| With () : | (-2)2 = (-2) × (-2) = 4 |
| Without () : | -22 = -(22) = - (2 × 2) = -4 |
| With () : | (ab)2 = ab × ab |
| Without () : | ab2 = a × (b)2 = a × b × b |
Thank you for using Apple Support Communities! I understand that your MacBook Air is starting up to a folder with a question mark. Having your MacBook Air power on as expected is important, and I would be happy to help.
The folder with a question mark means your Mac couldn't find a local or network-based startup disk. The next step would be to try connecting your MacBook Air to a different Wi-Fi network, then attempting to select your startup disk in macOS Recovery following the steps here:
If a flashing question mark appears when you start your Mac - Apple Support
Specifically, use this section:
If your Mac doesn't start up
If your Mac starts up to a flashing question mark, but then doesn't continue starting up, try these steps.
- Turn off your Mac by pressing and holding the power button for a few seconds.
- Press the power button once to turn your Mac back on. Immediately press and hold the Command and R keys on your keyboard to start your Mac from macOS Recovery. Keep these two keys held down until you see an Apple logo or globe.
- If prompted, select a Wi-Fi network to connect to the Internet as part of startup.
- After the macOS Utilities window appears, choose Startup Disk from the Apple menu.
- Select your startup disk, then click Restart.
If you don't see your startup disk in the Startup Disk window, close the window and try the next sections of this article.
If you encounter the -2100F error again when connected to a different Wi-Fi network, contact Apple via the link below:
Contact - Official Apple Support
Take care!
1.1 Understanding Exponentsmr. Mac's Page Manager
May 22, 2018 5:06 PM