remember that
![x^{\frac{a}{b}}=\sqrt[b]{x^a}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Csqrt%5Bb%5D%7Bx%5Ea%7D)
also ![x^{-a}=\frac{1}{x^a}](https://tex.z-dn.net/?f=x%5E%7B-a%7D%3D%5Cfrac%7B1%7D%7Bx%5Ea%7D)
and ![(a^b)^c=a^{bc}](https://tex.z-dn.net/?f=%28a%5Eb%29%5Ec%3Da%5E%7Bbc%7D)
so
![4^{\frac{2}{3}}](https://tex.z-dn.net/?f=4%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D)
first one, that one is clearly not equal since 0.25≠4
2nd one, 0.25=1/4, so
, which matches
3rd one,
, which matches
4th one
which matches
answer is ![0.25^{\frac{2}{3}}](https://tex.z-dn.net/?f=0.25%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D)
Answer:
multiplication ( 36) use vertical column method
Step-by-step explanation:
253×41
Use the Pythagorean theorem:
2)
![x^2+7^2=14^2\\\\x^2+49=196\qquad\text{subtract 49 from both sides}\\\\x^2=147\to x=\sqrt{147}\\\\x=\sqrt{49\cdot3}\\\\x=\sqrt{49}\cdot\sqrt3\\\\\boxed{x=7\sqrt3\ mi}](https://tex.z-dn.net/?f=x%5E2%2B7%5E2%3D14%5E2%5C%5C%5C%5Cx%5E2%2B49%3D196%5Cqquad%5Ctext%7Bsubtract%2049%20from%20both%20sides%7D%5C%5C%5C%5Cx%5E2%3D147%5Cto%20x%3D%5Csqrt%7B147%7D%5C%5C%5C%5Cx%3D%5Csqrt%7B49%5Ccdot3%7D%5C%5C%5C%5Cx%3D%5Csqrt%7B49%7D%5Ccdot%5Csqrt3%5C%5C%5C%5C%5Cboxed%7Bx%3D7%5Csqrt3%5C%20mi%7D)
4)
![x^2+9^2=(\sqrt{226})^2\\\\x^2+81=226\qquad\text{subtract 81 from both sides}\\\\x^2=145\to \boxed{x=\sqrt{145}\ km}](https://tex.z-dn.net/?f=x%5E2%2B9%5E2%3D%28%5Csqrt%7B226%7D%29%5E2%5C%5C%5C%5Cx%5E2%2B81%3D226%5Cqquad%5Ctext%7Bsubtract%2081%20from%20both%20sides%7D%5C%5C%5C%5Cx%5E2%3D145%5Cto%20%5Cboxed%7Bx%3D%5Csqrt%7B145%7D%5C%20km%7D)
Answer:
120.
Step-by-step explanation:
Using the Pythagoras theorem:
(30√2)^2 = x^2 + x^2 where x =length of each side of the square
1800 = 2x^2
x^2 = 900
x = 30.
So the perimeter = 4*30 = 120.