Answer:
14z+29y^3
Step-by-step explanation:
14z+12y^3+10y^3+7y^3
Combine like terms
14z+29y^3
Answer:
-3/7 > b
Step-by-step explanation:
2/7> b+5/7
Subtract 5/7 from each side
2/7-5/7> b+5/7-5/7
-3/7 > b
For this case we have the following expression:
![2(\sqrt[4]{16x})-2(\sqrt[4]{2y})+3(\sqrt[4]{81x})-4(\sqrt[4]{32y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B16x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B81x%7D%29-4%28%5Csqrt%5B4%5D%7B32y%7D%29)
Rewriting the numbers within the roots we have:
![2(\sqrt[4]{2*2*2*2x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3*3*3*3x})-4(\sqrt[4]{2*2*2*2*2y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B3%2A3%2A3%2A3x%7D%29-4%28%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2%2A2y%7D%29)
Then, by properties of powers we have:
![2(\sqrt[4]{2^4x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3^4x})-4(\sqrt[4]{2^42y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B2%5E4x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B3%5E4x%7D%29-4%28%5Csqrt%5B4%5D%7B2%5E42y%7D%29)
Then, by radical properties we have:
![2(2\sqrt[4]{x})-2(\sqrt[4]{2y})+3(3\sqrt[4]{x})-4(2\sqrt[4]{2y})](https://tex.z-dn.net/?f=2%282%5Csqrt%5B4%5D%7Bx%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%283%5Csqrt%5B4%5D%7Bx%7D%29-4%282%5Csqrt%5B4%5D%7B2y%7D%29)
Rewriting the expression we have:
![4\sqrt[4]{x}-2\sqrt[4]{2y}+9\sqrt[4]{x}-8\sqrt[4]{2y}](https://tex.z-dn.net/?f=4%5Csqrt%5B4%5D%7Bx%7D-2%5Csqrt%5B4%5D%7B2y%7D%2B9%5Csqrt%5B4%5D%7Bx%7D-8%5Csqrt%5B4%5D%7B2y%7D)
Finally, adding similar terms we have:
![(4+9)\sqrt[4]{x}-(2+8)\sqrt[4]{2y}](https://tex.z-dn.net/?f=%284%2B9%29%5Csqrt%5B4%5D%7Bx%7D-%282%2B8%29%5Csqrt%5B4%5D%7B2y%7D)
![13\sqrt[4]{x}-10\sqrt[4]{2y}](https://tex.z-dn.net/?f=13%5Csqrt%5B4%5D%7Bx%7D-10%5Csqrt%5B4%5D%7B2y%7D)
Answer:
The simplified form of the expression is:
![13\sqrt[4]{x}-10\sqrt[4]{2y}](https://tex.z-dn.net/?f=13%5Csqrt%5B4%5D%7Bx%7D-10%5Csqrt%5B4%5D%7B2y%7D)
To get 75 using 7, 5, 6, and 3 only once:
= (7+5) * 6 + 3
parentheses first
= 12 * 6 + 3
multiplication before addition
= 72 + 3
= 75
Without being given any constraints, I'm assuming multiplication and addition were allowed.
Hope this helps! :)