Hello Hewokai,
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.
2020 GROMACS user survey is now live.The survey will help the GROMACS developers to prioritise future GROMACS developments. We would like input from researchers who perform any and all forms of molecular dynamics and whose experience using GROMACS ranges from zero experience to expert active users. About This Quiz & Worksheet. Test your ability to simplify expressions using exponents in this quiz/worksheet combo. You will have five practice problems to solve, and you will need to know how to. November 2020 Freddie Mac Learning TOC Page i Table of Contents Chapter 1: Get Started with Workout Prospector Introduction.
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!
May 22, 2018 5:06 PM
Enter values into any two of the input fields to solve for the third.
What is an exponent?
Exponentiation is a mathematical operation, written as an, involving the base a and an exponent n. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times.
an = a × a × ... × a
n times
The calculator above accepts negative bases, but does not compute imaginary numbers. It also does not accept fractions, but can be used to compute fractional exponents, as long as the exponents are input in their decimal form.
Basic exponent laws and rules
When exponents that share the same base are multiplied, the exponents are added.
an × am = a(n+m)
EX: 22 × 24 = 4 × 16 = 64
22 × 24 = 2(2 + 4) = 26 = 64
When an exponent is negative, the negative sign is removed by reciprocating the base and raising it to the positive exponent.
| a(-n) = |
|
| EX: 2(-3) = 1 ÷ 2 ÷ 2 ÷ 2 | = |
|
| EX: 2(-3) = |
| = |
|
When exponents that share the same base are divided, the exponents are subtracted.
| = a(m - n) |
| EX: |
| = |
| = |
|
| = 2(2-4) = 2-2 = |
| = |
|
When exponents are raised to another exponent, the exponents are multiplied.
(am)n = a(m × n)
EX: (22)4 = 44 = 256
(22)4 = 2(2 × 4) = 28 = 256
When multiplied bases are raised to an exponent, the exponent is distributed to both bases.
(a × b)n = an × bn
EX: (2 × 4)2 = 82 = 64
(2 × 4)2 = 22 × 42 = 4 × 16 = 64
Similarly, when divided bases are raised to an exponent, the exponent is distributed to both bases.
| ( |
| )n | = |
|
| EX: ( |
| )2 | = |
| × |
| = |
|
| ( |
| )2 | = |
| = |
|
When an exponent is 1, the base remains the same.
a1 = a
1.1 Understanding Exponentsmr. Mac's Page Sign In
When an exponent is 0, the result of the exponentiation of any base will always be 1, although some debate surrounds 00 being 1 or undefined. For many applications, defining 00 as 1 is convenient.
a0 = 1
Shown below is an example of an argument for a0=1 using one of the previously mentioned exponent laws.
If an × am = a(n+m)
Then an × a0 = a(n+0) = an
Thus, the only way for an to remain unchanged by multiplication, and this exponent law to remain true, is for a0 to be 1.
1.1 Understanding Exponentsmr. Mac's Page Login
When an exponent is a fraction where the numerator is 1, the nth root of the base is taken. Shown below is an example with a fractional exponent where the numerator is not 1. It uses both the rule displayed, as well as the rule for multiplying exponents with like bases discussed above. Note that the calculator can calculate fractional exponents, but they must be entered into the calculator in decimal form.
1.1 Understanding Exponentsmr. Mac's Page Publishing
1.1 Understanding Exponentsmr. Mac's Page Manager
It is also possible to compute exponents with negative bases. They follow much the same rules as exponents with positive bases. Exponents with negative bases raised to positive integers are equal to their positive counterparts in magnitude, but vary based on sign. If the exponent is an even, positive integer, the values will be equal regardless of a positive or negative base. If the exponent is an odd, positive integer, the result will again have the same magnitude, but will be negative. While the rules for fractional exponents with negative bases are the same, they involve the use of imaginary numbers since it is not possible to take any root of a negative number. An example is provided below for reference, but please note that the calculator provided cannot compute imaginary numbers, and any inputs that result in an imaginary number will return the result 'NAN,' signifying 'not a number.' The numerical solution is essentially the same as the case with a positive base, except that the number must be denoted as imaginary.