Answer:
80
Step-by-step explanation:
the 80 is the tenth part so you do nothing its a trip up qustion
Ne demek istoyusun anlamadım
Answer:
![(3, 7)](https://tex.z-dn.net/?f=%283%2C%207%29)
Step-by-step explanation:
(4/3)P -(4/3)A + A = B . . . . . . add A
(4P -A)/3 = B . . . . . . . . . . . . . simplify
Then the coordinates of point B are ...
B = (4(1, 6) -(-5, 3))/3 = (9, 21)/3
B = (3, 7)
![\bf 343^{\frac{2}{3}}+36^{\frac{1}{2}}-256^{\frac{3}{4}}\qquad \begin{cases} 343=7\cdot 7\cdot 7\\ \qquad 7^3\\ 36=6\cdot 6\\ \qquad 6^2\\ 256=4\cdot 4\cdot 4\cdot 4\\ \qquad 4^4 \end{cases}\\\\\\ (7^3)^{\frac{2}{3}}+(6^2)^{\frac{1}{2}}-(4^4)^{\frac{3}{4}} \\\\\\ \sqrt[3]{(7^3)^2}+\sqrt[2]{(6^2)^1}-\sqrt[4]{(4^4)^3}\implies \sqrt[3]{(7^2)^3}+\sqrt[2]{(6^1)^2}-\sqrt[4]{(4^3)^4} \\\\\\ 7^2+6-4^3\implies 49+6-64\implies -9](https://tex.z-dn.net/?f=%5Cbf%20343%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%2B36%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D-256%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%5Cqquad%20%5Cbegin%7Bcases%7D%0A343%3D7%5Ccdot%207%5Ccdot%207%5C%5C%0A%5Cqquad%207%5E3%5C%5C%0A36%3D6%5Ccdot%206%5C%5C%0A%5Cqquad%206%5E2%5C%5C%0A256%3D4%5Ccdot%204%5Ccdot%204%5Ccdot%204%5C%5C%0A%5Cqquad%204%5E4%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%20%287%5E3%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%2B%286%5E2%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D-%284%5E4%29%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Csqrt%5B3%5D%7B%287%5E3%29%5E2%7D%2B%5Csqrt%5B2%5D%7B%286%5E2%29%5E1%7D-%5Csqrt%5B4%5D%7B%284%5E4%29%5E3%7D%5Cimplies%20%5Csqrt%5B3%5D%7B%287%5E2%29%5E3%7D%2B%5Csqrt%5B2%5D%7B%286%5E1%29%5E2%7D-%5Csqrt%5B4%5D%7B%284%5E3%29%5E4%7D%0A%5C%5C%5C%5C%5C%5C%0A7%5E2%2B6-4%5E3%5Cimplies%2049%2B6-64%5Cimplies%20-9)
to see what you can take out of the radical, you can always do a quick "prime factoring" of the values, that way you can break it in factors to see who is what.
The decimal representation of any number is a linear combination of powers of 10. In other words, given a number like 123.456, we can expand it as
![1\cdot10^2+2\cdot10^1+3\cdot10^0+4\cdot10^{-1}+5\cdot10^{-2}+6\cdot10^{-3}](https://tex.z-dn.net/?f=1%5Ccdot10%5E2%2B2%5Ccdot10%5E1%2B3%5Ccdot10%5E0%2B4%5Ccdot10%5E%7B-1%7D%2B5%5Ccdot10%5E%7B-2%7D%2B6%5Ccdot10%5E%7B-3%7D)
for any
, so the above is the same as
![100+20+3+\dfrac4{10}+\dfrac5{100}+\dfrac6{1000}=\dfrac{100000+20000+3000+400+50+6}{1000}=\dfrac{123456}{1000}](https://tex.z-dn.net/?f=100%2B20%2B3%2B%5Cdfrac4%7B10%7D%2B%5Cdfrac5%7B100%7D%2B%5Cdfrac6%7B1000%7D%3D%5Cdfrac%7B100000%2B20000%2B3000%2B400%2B50%2B6%7D%7B1000%7D%3D%5Cdfrac%7B123456%7D%7B1000%7D)
Similarly, we can write
![0.768=\dfrac{768}{1000}](https://tex.z-dn.net/?f=0.768%3D%5Cdfrac%7B768%7D%7B1000%7D)
Now it's a question of reducing the fraction as much as possible. We have
so
![\dfrac{768}{1000}=\dfrac{96\cdot8}{125\cdot8}=\dfrac{96}{125}](https://tex.z-dn.net/?f=%5Cdfrac%7B768%7D%7B1000%7D%3D%5Cdfrac%7B96%5Ccdot8%7D%7B125%5Ccdot8%7D%3D%5Cdfrac%7B96%7D%7B125%7D)