195 mm
Because is 19.5 cm = 195 mm
Answers:
See below
Step-by-step explanation:
First transformation
Reflection about the line y = 6.
This inter-converted Points A and C and Points B and D.
The coordinate transformations were (Fig. 1):
A: (-8, 8) ⟶ (-8, 4)
B: (-2, 8) ⟶ (-2, 4)
C: (-8, 4) ⟶ (-8, 8)
D: (-2, 4) ⟶ (-2, 8)
Second transformation
Translation 10 units to the right and 14 units down.
The coordinate transformations were (Fig. 2):
A: (-8, 4) ⟶ (2, -10)
B: (-2, 4) ⟶ (8, -10)
C: (-8, 8) ⟶ (2, -6)
D: (-2, 8) ⟶ (8, -6)
The transformations were:
- Reflection about the line y = 6
- Translation 10 units to the right and 14 units down
ANSWER
![3 {x}^{2} y \sqrt[4]{y}](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20y%20%5Csqrt%5B4%5D%7By%7D%20)
EXPLANATION
We want to simplify:
![\sqrt[4]{81 {x}^{8} {y}^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81%20%7Bx%7D%5E%7B8%7D%20%7By%7D%5E%7B5%7D%20%20%7D%20)
We can split the radical sign to obtain:
![\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7Bx%7D%5E%7B8%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B5%7D%20%7D%20)
Or
![\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7Bx%7D%5E%7B8%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B4%7D%20%20%5Ctimes%20y%7D%20)
![\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B81%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7Bx%7D%5E%7B8%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B4%7D%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7By%7D%20)
![\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%20%7B3%7D%5E%7B4%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7Bx%7D%5E%7B8%7D%20%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7B%20%7By%7D%5E%7B4%7D%7D%20%20%5Ctimes%20%20%5Csqrt%5B4%5D%7By%7D%20)
Recall that:
![\sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7B%20%7Ba%7D%5E%7Bm%7D%20%7D%20%20%3D%20%20%7Ba%7D%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%20%7D%20%20)
![{3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y}](https://tex.z-dn.net/?f=%7B3%7D%5E%7B4%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B4%7D%20%7D%20%20%5Ctimes%20%20%7Bx%7D%5E%7B8%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%7D%20%20%5Ctimes%20%20%7By%7D%5E%7B4%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B4%7D%20%7D%5Ctimes%20%20%5Csqrt%5B4%5D%7By%7D%20)
![3 {x}^{2} y \sqrt[4]{y}](https://tex.z-dn.net/?f=3%20%7Bx%7D%5E%7B2%7D%20y%20%5Csqrt%5B4%5D%7By%7D%20)
11/14 minus 7/14 is equal to 4/14.