Answer:
24
Step-by-step explanation:
18+12-6
For this case we have the following expression:
![\frac {216 ^ {n-2}} {(\frac {1} {36}) ^ {3n}} = 216](https://tex.z-dn.net/?f=%5Cfrac%20%7B216%20%5E%20%7Bn-2%7D%7D%20%7B%28%5Cfrac%20%7B1%7D%20%7B36%7D%29%20%5E%20%7B3n%7D%7D%20%3D%20216)
We multiply both sides by: ![(\frac {1} {36}) ^ {3n}](https://tex.z-dn.net/?f=%28%5Cfrac%20%7B1%7D%20%7B36%7D%29%20%5E%20%7B3n%7D)
![216 ^ {n-2} = 216 * (\frac {1} {36}) ^ {3n}](https://tex.z-dn.net/?f=216%20%5E%20%7Bn-2%7D%20%3D%20216%20%2A%20%28%5Cfrac%20%7B1%7D%20%7B36%7D%29%20%5E%20%7B3n%7D)
We divide both sides by 216:
![\frac {216 ^ {n-2}} {216} = (\frac {1} {36}) ^ {3n}](https://tex.z-dn.net/?f=%5Cfrac%20%7B216%20%5E%20%7Bn-2%7D%7D%20%7B216%7D%20%3D%20%28%5Cfrac%20%7B1%7D%20%7B36%7D%29%20%5E%20%7B3n%7D)
To divide powers of the same base, we place the same base and subtract the exponents:
![216 ^ {n-2-1} = (\frac {1} {36}) ^ {3n}\\216 ^ {n-3} = (\frac {1} {36}) ^ {3n}](https://tex.z-dn.net/?f=216%20%5E%20%7Bn-2-1%7D%20%3D%20%28%5Cfrac%20%7B1%7D%20%7B36%7D%29%20%5E%20%7B3n%7D%5C%5C216%20%5E%20%7Bn-3%7D%20%3D%20%28%5Cfrac%20%7B1%7D%20%7B36%7D%29%20%5E%20%7B3n%7D)
Rewriting:
![(6 ^ 3) ^ {n-3} = (\frac {1} {6 ^ 2}) ^ {3n}\\6 ^ {3n-9} = \frac {1} {6 ^ {6n}}\\6^{ 3n-9} * 6^{ 6n} = 1](https://tex.z-dn.net/?f=%286%20%5E%203%29%20%5E%20%7Bn-3%7D%20%3D%20%28%5Cfrac%20%7B1%7D%20%7B6%20%5E%202%7D%29%20%5E%20%7B3n%7D%5C%5C6%20%5E%20%7B3n-9%7D%20%3D%20%5Cfrac%20%7B1%7D%20%7B6%20%5E%20%7B6n%7D%7D%5C%5C6%5E%7B%203n-9%7D%20%2A%206%5E%7B%206n%7D%20%3D%201)
To multiply powers of the same base, we place the same base and add the exponents:
![6^{ 3n-9 + 6n} = 1\\6^{ 9n-9} = 1](https://tex.z-dn.net/?f=6%5E%7B%203n-9%20%2B%206n%7D%20%3D%201%5C%5C6%5E%7B%209n-9%7D%20%3D%201)
We know that any number raised to zero is 1, ![a ^ 0 = 1.](https://tex.z-dn.net/?f=a%20%5E%200%20%3D%201.)
So, for equality to be true:
![9n-9 = 0\\9n = 9\\n = \frac {9} {9}\\n = 1](https://tex.z-dn.net/?f=9n-9%20%3D%200%5C%5C9n%20%3D%209%5C%5Cn%20%3D%20%5Cfrac%20%7B9%7D%20%7B9%7D%5C%5Cn%20%3D%201)
Answer:
![n = 1](https://tex.z-dn.net/?f=n%20%3D%201)
Answer:
False
Step-by-step explanation:
Order of magnitude can mean different things in different contexts. In math, when we talk about order of magnitude, we generally mean the base-10 logarithm.
__
<h3>population order of magnitude</h3>
The population of the US is estimated at about 3.32×10^8 on 1 Jan 2022. The base-10 log of this number is about 8.52.
The order of magnitude of the US population is about 8.5, not 4.
Answer:
answer is in explanation
Step-by-step explanation:
It could be? the 7 could be 7 to literally any number soooo