Answer:
![\sqrt{8x^7y^8](https://tex.z-dn.net/?f=%5Csqrt%7B8x%5E7y%5E8)
![= 2x^3y^4 * \sqrt{2x}](https://tex.z-dn.net/?f=%3D%202x%5E3y%5E4%20%2A%20%5Csqrt%7B2x%7D)
Step-by-step explanation:
Given
![\sqrt{8x^7y^8](https://tex.z-dn.net/?f=%5Csqrt%7B8x%5E7y%5E8)
Required
Evaluate
![\sqrt{8x^7y^8](https://tex.z-dn.net/?f=%5Csqrt%7B8x%5E7y%5E8)
Separate each factor with multiplication sign
![\sqrt{8*x^7*y^8](https://tex.z-dn.net/?f=%5Csqrt%7B8%2Ax%5E7%2Ay%5E8)
Express 8 as 4 * 2 and
as ![x^6 * x](https://tex.z-dn.net/?f=x%5E6%20%2A%20x)
![\sqrt{4 * 2 *x^6 * x*y^8](https://tex.z-dn.net/?f=%5Csqrt%7B4%20%2A%202%20%2Ax%5E6%20%2A%20x%2Ay%5E8)
Split each factor
![\sqrt{4} * \sqrt{2} *\sqrt{x^6} * \sqrt{x}*\sqrt{y^8}](https://tex.z-dn.net/?f=%5Csqrt%7B4%7D%20%2A%20%5Csqrt%7B2%7D%20%2A%5Csqrt%7Bx%5E6%7D%20%2A%20%5Csqrt%7Bx%7D%2A%5Csqrt%7By%5E8%7D)
Evaluate ![\sqrt4](https://tex.z-dn.net/?f=%5Csqrt4)
![2 * \sqrt{2} *\sqrt{x^6} * \sqrt{x}*\sqrt{y^8}](https://tex.z-dn.net/?f=2%20%2A%20%5Csqrt%7B2%7D%20%2A%5Csqrt%7Bx%5E6%7D%20%2A%20%5Csqrt%7Bx%7D%2A%5Csqrt%7By%5E8%7D)
Apply law of indices:
![2 * \sqrt{2} * x^{6*\frac{1}{2}} * \sqrt{x} * y^{8*\frac{1}{2}}](https://tex.z-dn.net/?f=2%20%2A%20%5Csqrt%7B2%7D%20%2A%20x%5E%7B6%2A%5Cfrac%7B1%7D%7B2%7D%7D%20%2A%20%5Csqrt%7Bx%7D%20%2A%20y%5E%7B8%2A%5Cfrac%7B1%7D%7B2%7D%7D)
![2 * \sqrt{2} * x^3 * \sqrt{x} * y^4](https://tex.z-dn.net/?f=2%20%2A%20%5Csqrt%7B2%7D%20%2A%20x%5E3%20%2A%20%5Csqrt%7Bx%7D%20%2A%20y%5E4)
Reorder
![2* x^3 * y^4 * \sqrt{2} * \sqrt{x}](https://tex.z-dn.net/?f=2%2A%20x%5E3%20%2A%20y%5E4%20%2A%20%5Csqrt%7B2%7D%20%20%2A%20%5Csqrt%7Bx%7D)
![2x^3y^4 * \sqrt{2} * \sqrt{x}](https://tex.z-dn.net/?f=2x%5E3y%5E4%20%2A%20%5Csqrt%7B2%7D%20%20%2A%20%5Csqrt%7Bx%7D)
![2x^3y^4 * \sqrt{2*x}](https://tex.z-dn.net/?f=2x%5E3y%5E4%20%2A%20%5Csqrt%7B2%2Ax%7D)
![2x^3y^4 * \sqrt{2x}](https://tex.z-dn.net/?f=2x%5E3y%5E4%20%2A%20%5Csqrt%7B2x%7D)
![2x^3y^4 \sqrt {2x](https://tex.z-dn.net/?f=2x%5E3y%5E4%20%5Csqrt%20%7B2x)
Hence:
![\sqrt{8x^7y^8](https://tex.z-dn.net/?f=%5Csqrt%7B8x%5E7y%5E8)
![= 2x^3y^4 * \sqrt{2x}](https://tex.z-dn.net/?f=%3D%202x%5E3y%5E4%20%2A%20%5Csqrt%7B2x%7D)
Number of large boxes:
50
Number of small boxes: 65
There are eight cities on the list.
The number of groups of 2 is (8·7)/2 = 28
The number of groups of 3 is (8·7·6)/(3!) = 56
The number of groups of 4 is (8·7·6·5)/(4!) = 70
The number of groups of 5 is (8·7·6·5·4)/(5!) = 56
The number of groups of 6 is (8·7·6·5·4·3)/(6!) = 28
The number of groups of 7 is (8·7·6·5·4·3·2)/(7!) = 8
So there are (28+56+70+56+28+8) = 246 ways to visit "some" of them.
There's only one way to visit "all" of them, and
there's only one way to visit "none" of them.
So, all together, Louise has 248 travel options.
If she decides to visit Chicago, I will show her a good time.
Answer:
1372
Step-by-step explanation:
Because 980 divided by 5 is 196 and 196 x 5 = 980
So you take 196 and multiply it by 5 and it's 1372
Hope this helps :)
Subtract 3t from the equation to get 2t=-7. Multiply by three to find that 6t=-21.